main.cpp 36.5 KB
Newer Older
incardon's avatar
incardon committed
1
/*!
incardon's avatar
incardon committed
2
 * \page Vector_7_sph_dlb Vector 7 SPH Dam break simulation with Dynamic load balacing
incardon's avatar
incardon committed
3 4 5 6 7 8 9 10
 *
 *
 * [TOC]
 *
 *
 * # SPH with Dynamic load Balancing # {#SPH_dlb}
 *
 *
incardon's avatar
incardon committed
11 12 13
 * This example show the classical SPH Dam break simulation with Load Balancing and Dynamic load balancing. With
 * Load balancing and Dynamic load balancing we indicate the possibility of the system to re-adapt the domain
 * decomposition to keep all the processor load and reduce idle time.
incardon's avatar
incardon committed
14 15 16 17
 *
 * ## inclusion ## {#e0_v_inclusion}
 *
 * In order to use distributed vectors in our code we have to include the file Vector/vector_dist.hpp
incardon's avatar
incardon committed
18 19
 * we also include DrawParticles that has nice utilities to draw particles in parallel accordingly
 * to simple shapes
incardon's avatar
incardon committed
20 21 22 23 24
 *
 * \snippet Vector/7_SPH_dlb/main.cpp inclusion
 *
 */

incardon's avatar
incardon committed
25 26 27
//#define SE_CLASS1
//#define STOP_ON_ERROR

incardon's avatar
incardon committed
28 29 30
//! \cond [inclusion] \endcond
#include "Vector/vector_dist.hpp"
#include <math.h>
incardon's avatar
incardon committed
31
#include "Draw/DrawParticles.hpp"
incardon's avatar
incardon committed
32 33
//! \cond [inclusion] \endcond

incardon's avatar
incardon committed
34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71
/*!
 * \page Vector_7_sph_dlb Vector 7 SPH Dam break  simulation with Dynamic load balacing
 *
 * ## Parameters {#e7_sph_parameters}
 *
 * The SPH formulation used in this example code follow these equations
 *
 * \f$\frac{dv_a}{dt} = - \sum_{b = NN(a) } m_b \left(\frac{P_a + P_b}{\rho_a \rho_b} + \Pi_{ab} \right) \nabla_{a} W_{ab} + g  \tag{1} \f$
 *
 * \f$\frac{d\rho_a}{dt} =  \sum_{b = NN(a) } m_b v_{ab} \cdot \nabla_{a} W_{ab} \tag{2} \f$
 *
 * \f$ P_a = b \left[ \left( \frac{\rho_a}{\rho_{0}} \right)^{\gamma} - 1 \right] \tag{3} \f$
 *
 * with
 *
 * \f$ \Pi_{ab} =  \begin{cases} - \frac {\alpha \bar{c_{ab}} \mu_{ab} }{\bar{\rho_{ab}} } & v_{ab} \cdot r_{ab} > 0 \\ 0 & v_{ab} \cdot r_{ab} < 0 \end{cases} \tag{4}\f$
 *
 * and the constants defined as
 *
 * \f$ b = \frac{c_{s}^{2} \rho_0}{\gamma} \tag{5} \f$
 *
 * \f$ c_s = \sqrt{g \cdot h_{swl}} \tag{6} \f$
 *
 * While the particle kernel support is given by
 *
 * \f$ H = \sqrt{3 \cdot dp} \tag{7} \f$
 *
 * Explain the equations is out of the context of this tutorial. An introduction
 * can be found in the original Monghagan SPH paper. In this example we use the version
 * used by Dual-SPH (http://www.dual.sphysics.org/). A summary of the equation and constants can be founded in
 * their User Manual and the XML user Manual.
 * In the following we define all the constants required by the simulation
 *
 * \snippet Vector/7_SPH_dlb/main.cpp sim parameters
 *
 */

/*! \cond [sim parameters] \endcond */
incardon's avatar
incardon committed
72

incardon's avatar
incardon committed
73
// A constant to indicate boundary particles
incardon's avatar
incardon committed
74 75
#define BOUNDARY 0

incardon's avatar
incardon committed
76 77
// A constant to indicate fluid particles
#define FLUID 1
incardon's avatar
incardon committed
78

incardon's avatar
incardon committed
79
// initial spacing between particles dp in the formulas
incardon's avatar
incardon committed
80
const double dp = 0.0085;
incardon's avatar
incardon committed
81 82
// Maximum height of the fluid water
// is coing to be calculated and filled later on
incardon's avatar
incardon committed
83
double h_swl = 0.0;
incardon's avatar
incardon committed
84 85

// in the formulas indicated with c_s (constant used to calculate the sound speed)
incardon's avatar
incardon committed
86
const double coeff_sound = 20.0;
incardon's avatar
incardon committed
87 88

// gamma in the formulas
incardon's avatar
incardon committed
89
const double gamma_ = 7.0;
incardon's avatar
incardon committed
90 91

// sqrt(3.0*dp*dp) support of the kernel
incardon's avatar
incardon committed
92
const double H = 0.0147224318643;
incardon's avatar
incardon committed
93 94

// Eta in the formulas
incardon's avatar
incardon committed
95
const double Eta2 = 0.01 * H*H;
incardon's avatar
incardon committed
96 97


incardon's avatar
incardon committed
98 99
const double visco = 0.1;
double cbar = 0.0;
incardon's avatar
incardon committed
100 101

// Mass of the fluid particles
incardon's avatar
incardon committed
102
const double MassFluid = 0.000614125;
incardon's avatar
incardon committed
103 104

// Mass of the boundary particles
incardon's avatar
incardon committed
105
const double MassBound = 0.000614125;
incardon's avatar
incardon committed
106 107 108 109 110

// End simulation time
const double t_end = 1.5;

// Gravity acceleration
incardon's avatar
incardon committed
111
const double gravity = 9.81;
incardon's avatar
incardon committed
112 113

// Reference densitu 1000Kg/m^3
incardon's avatar
incardon committed
114
const double rho_zero = 1000.0;
incardon's avatar
incardon committed
115 116

// Filled later require h_swl, it is b in the formulas
incardon's avatar
incardon committed
117
double B = 0.0;
incardon's avatar
incardon committed
118 119

// Constant used to define time integration
incardon's avatar
incardon committed
120
const double CFLnumber = 0.2;
incardon's avatar
incardon committed
121 122

// Minimum T
incardon's avatar
incardon committed
123 124
const double DtMin = 0.00001;

incardon's avatar
incardon committed
125 126 127 128 129 130
// Minimum Rho allowed
const double RhoMin = 700.0;

// Maximum Rho allowed
const double RhoMax = 1300.0;

incardon's avatar
incardon committed
131 132 133
// Filled in initialization
double max_fluid_height = 0.0;

incardon's avatar
incardon committed
134 135 136
// Properties

// FLUID or BOUNDARY
incardon's avatar
incardon committed
137
const size_t type = 0;
incardon's avatar
incardon committed
138 139

// Density
incardon's avatar
incardon committed
140
const int rho = 1;
incardon's avatar
incardon committed
141 142

// Density at step n-1
incardon's avatar
incardon committed
143
const int rho_prev = 2;
incardon's avatar
incardon committed
144 145

// Pressure
incardon's avatar
incardon committed
146
const int Pressure = 3;
incardon's avatar
incardon committed
147 148

// Delta rho calculated in the force calculation
incardon's avatar
incardon committed
149
const int drho = 4;
incardon's avatar
incardon committed
150 151

// calculated force
incardon's avatar
incardon committed
152
const int force = 5;
incardon's avatar
incardon committed
153 154

// velocity
incardon's avatar
incardon committed
155
const int velocity = 6;
incardon's avatar
incardon committed
156 157

// velocity at previous step
incardon's avatar
incardon committed
158 159
const int velocity_prev = 7;

incardon's avatar
incardon committed
160 161
/*! \cond [vector_dist_def] \endcond */

incardon's avatar
incardon committed
162 163 164 165 166 167
// Type of the vector containing particles
typedef vector_dist<3,double,aggregate<size_t,double,  double,    double,     double,     double[3], double[3], double[3]>> particles;
//                                       |      |        |          |            |            |         |            |
//                                       |      |        |          |            |            |         |            |
//                                     type   density   density    Pressure    delta       force     velocity    velocity
//                                                      at n-1                 density                           at n - 1
incardon's avatar
incardon committed
168

incardon's avatar
incardon committed
169
/*! \cond [vector_dist_def] \endcond */
incardon's avatar
incardon committed
170

incardon's avatar
incardon committed
171
/*! \cond [model custom] \endcond */
incardon's avatar
incardon committed
172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188

struct ModelCustom
{
	template<typename Decomposition, typename vector> inline void addComputation(Decomposition & dec, const vector & vd, size_t v, size_t p)
	{
		if (vd.template getProp<type>(p) == FLUID)
			dec.addComputationCost(v,3);
		else
			dec.addComputationCost(v,2);
	}

	template<typename Decomposition> inline void applyModel(Decomposition & dec, size_t v)
	{
		dec.setSubSubDomainComputationCost(v, dec.getSubSubDomainComputationCost(v) * dec.getSubSubDomainComputationCost(v));
	}
};

incardon's avatar
incardon committed
189
/*! \cond [model custom] \endcond */
incardon's avatar
incardon committed
190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207

/*!
 * \page Vector_7_sph_dlb Vector 7 SPH Dam break  simulation with Dynamic load balacing
 *
 * ## Equation of state and SPH Kernels {#e7_sph_equation_state}
 *
 * This function implement the formula 3 in the set of equations. It calculate the
 * pressure of each particle based on the local density of each particle.
 *
 * \snippet Vector/7_SPH_dlb/main.cpp eq_state_and_ker
 *
 */

/*! \cond [eq_state_and_ker] \endcond */


inline void EqState(particles & vd)
{
incardon's avatar
incardon committed
208 209 210 211 212 213 214 215 216 217 218 219 220
	auto it = vd.getDomainIterator();

	while (it.isNext())
	{
		auto a = it.get();

		double rho_a = vd.template getProp<rho>(a);
		double rho_frac = rho_a / rho_zero;

		vd.template getProp<Pressure>(a) = B*( rho_frac*rho_frac*rho_frac*rho_frac*rho_frac*rho_frac*rho_frac - 1.0);

		++it;
	}
incardon's avatar
incardon committed
221
}
incardon's avatar
incardon committed
222

incardon's avatar
incardon committed
223
/*! \cond [eq_state_and_ker] \endcond */
incardon's avatar
incardon committed
224

incardon's avatar
incardon committed
225 226 227 228 229 230 231 232 233 234 235
/*!
 * \page Vector_7_sph_dlb Vector 7 SPH Dam break  simulation with Dynamic load balancing
 *
 * This function define the Cubic kernel or \f$ W_{ab} \f$ in the set of equations. The cubic kernel is
 * defined as
 *
 * \f$ \begin{cases} 1.0 - \frac{3}{2} q^2 + \frac{3}{4} q^3 & 0 < q < 1 \\ (2 - q)^3 & 1 < q < 2 \\ 0 & q > 2 \end{cases} \f$
 *
 * \snippet Vector/7_SPH_dlb/main.cpp kernel_sph
 *
 */
incardon's avatar
incardon committed
236

incardon's avatar
incardon committed
237
/*! \cond [kernel_sph] \endcond */
incardon's avatar
incardon committed
238 239 240 241 242 243 244 245 246 247 248 249 250 251 252

const double a2 = 1.0/M_PI/H/H/H;

inline double Wab(double r)
{
	r /= H;

	if (r < 1.0)
		return (1.0 - 3.0/2.0*r*r + 3.0/4.0*r*r*r)*a2;
	else if (r < 2.0)
		return (1.0/4.0*(2.0 - r*r)*(2.0 - r*r)*(2.0 - r*r))*a2;
	else
		return 0.0;
}

incardon's avatar
incardon committed
253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275
/*! \cond [kernel_sph] \endcond */

/*!
 * \page Vector_7_sph_dlb Vector 7 SPH Dam break  simulation with Dynamic load balancing
 *
 * This function define the derivative of the Cubic kernel function \f$ W_{ab} \f$ in the set of equations.
 *
 * \f$ \nabla W_{ab} = \beta (x,y,z)  \f$
 *
 * \f$ \beta = \begin{cases} (c_1 q + d_1 q^2) & 0 < q < 1 \\ c_2 (2 - q)^2  & 1 < q < 2 \end{cases} \f$
 *
 * \snippet Vector/7_SPH_dlb/main.cpp kernel_sph_der
 *
 */

/*! \cond [kernel_sph_der] \endcond */

const double c1 = -3.0/M_PI/H/H/H/H;
const double d1 = 9.0/4.0/M_PI/H/H/H/H;
const double c2 = -3.0/4.0/M_PI/H/H/H/H;
const double a2_4 = 0.25*a2;
// Filled later
double W_dap = 0.0;
incardon's avatar
incardon committed
276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306

inline void DWab(Point<3,double> & dx, Point<3,double> & DW, double r, bool print)
{
	const double qq=r/H;

	if (qq < 1.0)
	{
		double qq2 = qq * qq;
		double fac = (c1*qq + d1*qq2)/r;

		DW.get(0) = fac*dx.get(0);
		DW.get(1) = fac*dx.get(1);
		DW.get(2) = fac*dx.get(2);
	}
	else if (qq < 2.0)
	{
		double wqq = (2.0 - qq);
		double fac = c2 * wqq * wqq / r;

		DW.get(0) = fac * dx.get(0);
		DW.get(1) = fac * dx.get(1);
		DW.get(2) = fac * dx.get(2);
	}
	else
	{
		DW.get(0) = 0.0;
		DW.get(1) = 0.0;
		DW.get(2) = 0.0;
	}
}

incardon's avatar
incardon committed
307 308 309 310 311 312 313
/*! \cond [kernel_sph_der] \endcond */

/*!
 * \page Vector_7_sph_dlb Vector 7 SPH Dam break  simulation with Dynamic load balancing
 *
 * This function define the Tensile term. An explanation of the Tensile term is out of the
 * context of this tutorial, but in brief is an additional repulsive term that avoid the particles
incardon's avatar
incardon committed
314
 * to get too near. Can be considered at small scale like a repulsive force that avoid
incardon's avatar
incardon committed
315 316 317 318 319 320 321 322 323 324
 * particles to get too close like the Lennard-Jhonned potential at atomistic level. A good
 * reference is the Monaghan paper "SPH without a Tensile Instability"
 *
 * \snippet Vector/7_SPH_dlb/main.cpp tensile_term
 *
 *
 */

/*! \cond [tensile_term] \endcond */

incardon's avatar
incardon committed
325
// Tensile correction
incardon's avatar
incardon committed
326
inline double Tensile(double r, double rhoa, double rhob, double prs1, double prs2)
incardon's avatar
incardon committed
327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354
{
	const double qq=r/H;
	//-Cubic Spline kernel
	double wab;
	if(r>H)
	{
		double wqq1=2.0f-qq;
		double wqq2=wqq1*wqq1;

		wab=a2_4*(wqq2*wqq1);
	}
	else
	{
	    double wqq2=qq*qq;
	    double wqq3=wqq2*qq;

	    wab=a2*(1.0f-1.5f*wqq2+0.75f*wqq3);
	}

	//-Tensile correction.
	double fab=wab*W_dap;
	fab*=fab; fab*=fab; //fab=fab^4
	const double tensilp1=(prs1/(rhoa*rhoa))*(prs1>0? 0.01: -0.2);
	const double tensilp2=(prs2/(rhob*rhob))*(prs2>0? 0.01: -0.2);

	return (fab*(tensilp1+tensilp2));
}

incardon's avatar
incardon committed
355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371
/*! \cond [tensile_term] \endcond */


/*!
 *
 * \page Vector_7_sph_dlb Vector 7 SPH Dam break  simulation with Dynamic load balancing
 *
 * This function is the implementation of the viscous term \f$ \Pi_{ab} \f$
 *
 * \snippet Vector/7_SPH_dlb/main.cpp viscous_term
 *
 *
 */

/*! \cond [viscous_term] \endcond */

inline double Pi(const Point<3,double> & dr, double rr2, Point<3,double> & dv, double rhoa, double rhob, double massb, double & visc)
incardon's avatar
incardon committed
372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388
{
	const double dot = dr.get(0)*dv.get(0) + dr.get(1)*dv.get(1) + dr.get(2)*dv.get(2);
	const double dot_rr2 = dot/(rr2+Eta2);
	visc=std::max(dot_rr2,visc);

	if(dot < 0)
	{
		const float amubar=H*dot_rr2;
		const float robar=(rhoa+rhob)*0.5f;
		const float pi_visc=(-visco*cbar*amubar/robar);

		return pi_visc;
    }
	else
		return 0.0;
}

incardon's avatar
incardon committed
389 390 391 392 393 394 395 396 397 398 399 400 401 402 403 404 405
/*! \cond [viscous_term] \endcond */

/*!
 *
 * \page Vector_7_sph_dlb Vector 7 SPH Dam break  simulation with Dynamic load balancing
 *
 * ## Force calculation {#e7_force_calc}
 *
 * Calculate forces. It calculate equation 1 and 2 in the set of formulas
 *
 * \snippet Vector/7_SPH_dlb/main.cpp calc_forces
 *
 *
 */

/*! \cond [calc_forces] \endcond */

incardon's avatar
incardon committed
406 407 408 409 410
template<typename CellList> inline double calc_forces(particles & vd, CellList & NN, double & max_visc)
{
	auto part = vd.getDomainIterator();
	double visc = 0;

incardon's avatar
incardon committed
411
	// Update the cell-list
incardon's avatar
incardon committed
412 413
	vd.updateCellList(NN);

incardon's avatar
incardon committed
414
	// For each particle ...
incardon's avatar
incardon committed
415 416
	while (part.isNext())
	{
incardon's avatar
incardon committed
417
		// ... a
incardon's avatar
incardon committed
418 419 420 421 422
		auto a = part.get();

		// Get the position xp of the particle
		Point<3,double> xa = vd.getPos(a);

incardon's avatar
incardon committed
423
		// Take the mass of the particle dependently if it is FLUID or BOUNDARY
incardon's avatar
incardon committed
424
		double massa = (vd.getProp<type>(a) == FLUID)?MassFluid:MassBound;
incardon's avatar
incardon committed
425 426

		// Get the density of the of the particle a
incardon's avatar
incardon committed
427
		double rhoa = vd.getProp<rho>(a);
incardon's avatar
incardon committed
428 429

		// Get the pressure of the particle a
incardon's avatar
incardon committed
430
		double Pa = vd.getProp<Pressure>(a);
incardon's avatar
incardon committed
431 432

		// Get the Velocity of the particle a
incardon's avatar
incardon committed
433 434
		Point<3,double> va = vd.getProp<velocity>(a);

incardon's avatar
incardon committed
435
		// Reset the force counter (- gravity on zeta direction)
incardon's avatar
incardon committed
436 437 438 439 440
		vd.template getProp<force>(a)[0] = 0.0;
		vd.template getProp<force>(a)[1] = 0.0;
		vd.template getProp<force>(a)[2] = -gravity;
		vd.template getProp<drho>(a) = 0.0;

incardon's avatar
incardon committed
441 442 443 444 445 446
		// We threat FLUID particle differently from BOUNDARY PARTICLES ...
		if (vd.getProp<type>(a) != FLUID)
		{
			// If it is a boundary particle calculate the delta rho based on equation 2
			// This require to run across the neighborhoods particles of a
			auto Np = NN.template getNNIterator<NO_CHECK>(NN.getCell(vd.getPos(a)));
incardon's avatar
incardon committed
447

incardon's avatar
incardon committed
448 449 450 451 452
			// For each neighborhood particle
			while (Np.isNext() == true)
			{
				// ... q
				auto b = Np.get();
incardon's avatar
incardon committed
453

incardon's avatar
incardon committed
454 455
				// Get the position xp of the particle
				Point<3,double> xb = vd.getPos(b);
incardon's avatar
incardon committed
456

incardon's avatar
incardon committed
457 458
				// if (p == q) skip this particle
				if (a.getKey() == b)	{++Np; continue;};
incardon's avatar
incardon committed
459

incardon's avatar
incardon committed
460 461
				// get the mass of the particle
				double massb = (vd.getProp<type>(b) == FLUID)?MassFluid:MassBound;
incardon's avatar
incardon committed
462

incardon's avatar
incardon committed
463 464
				// Get the velocity of the particle b
				Point<3,double> vb = vd.getProp<velocity>(b);
incardon's avatar
incardon committed
465

incardon's avatar
incardon committed
466 467 468
				// Get the pressure and density of particle b
				double Pb = vd.getProp<Pressure>(b);
				double rhob = vd.getProp<rho>(b);
incardon's avatar
incardon committed
469

incardon's avatar
incardon committed
470 471 472 473
				// Get the distance between p and q
				Point<3,double> dr = xa - xb;
				// take the norm of this vector
				double r2 = norm2(dr);
incardon's avatar
incardon committed
474

incardon's avatar
incardon committed
475 476 477 478 479
				// If the particles interact ...
				if (r2 < 4.0*H*H)
				{
					// ... calculate delta rho
					double r = sqrt(r2);
incardon's avatar
incardon committed
480

incardon's avatar
incardon committed
481
					Point<3,double> dv = va - vb;
incardon's avatar
incardon committed
482

incardon's avatar
incardon committed
483 484
					Point<3,double> DW;
					DWab(dr,DW,r,false);
incardon's avatar
incardon committed
485

incardon's avatar
incardon committed
486 487 488
					const double dot = dr.get(0)*dv.get(0) + dr.get(1)*dv.get(1) + dr.get(2)*dv.get(2);
					const double dot_rr2 = dot/(r2+Eta2);
					max_visc=std::max(dot_rr2,max_visc);
incardon's avatar
incardon committed
489

incardon's avatar
incardon committed
490 491
					vd.getProp<drho>(a) += massb*(dv.get(0)*DW.get(0)+dv.get(1)*DW.get(1)+dv.get(2)*DW.get(2));
				}
incardon's avatar
incardon committed
492

incardon's avatar
incardon committed
493
				++Np;
incardon's avatar
incardon committed
494 495
			}
		}
incardon's avatar
incardon committed
496
		else
incardon's avatar
incardon committed
497
		{
incardon's avatar
incardon committed
498
			// If it is a fluid particle calculate based on equation 1 and 2
incardon's avatar
incardon committed
499

incardon's avatar
incardon committed
500 501
			// Get an iterator over the neighborhood particles of p
			auto Np = NN.template getNNIterator<NO_CHECK>(NN.getCell(vd.getPos(a)));
incardon's avatar
incardon committed
502

incardon's avatar
incardon committed
503 504 505 506 507
			// For each neighborhood particle
			while (Np.isNext() == true)
			{
				// ... q
				auto b = Np.get();
incardon's avatar
incardon committed
508

incardon's avatar
incardon committed
509 510
				// Get the position xp of the particle
				Point<3,double> xb = vd.getPos(b);
incardon's avatar
incardon committed
511

incardon's avatar
incardon committed
512 513
				// if (p == q) skip this particle
				if (a.getKey() == b)	{++Np; continue;};
incardon's avatar
incardon committed
514

incardon's avatar
incardon committed
515 516 517 518
				double massb = (vd.getProp<type>(b) == FLUID)?MassFluid:MassBound;
				Point<3,double> vb = vd.getProp<velocity>(b);
				double Pb = vd.getProp<Pressure>(b);
				double rhob = vd.getProp<rho>(b);
incardon's avatar
incardon committed
519

incardon's avatar
incardon committed
520 521 522 523
				// Get the distance between p and q
				Point<3,double> dr = xa - xb;
				// take the norm of this vector
				double r2 = norm2(dr);
incardon's avatar
incardon committed
524

incardon's avatar
incardon committed
525 526 527 528 529 530 531 532 533 534 535 536 537 538 539 540 541 542 543 544 545
				// if they interact
				if (r2 < 4.0*H*H)
				{
					double r = sqrt(r2);

					Point<3,double> v_rel = va - vb;

					Point<3,double> DW;
					DWab(dr,DW,r,false);

					double factor = - massb*((vd.getProp<Pressure>(a) + vd.getProp<Pressure>(b)) / (rhoa * rhob) + Tensile(r,rhoa,rhob,Pa,Pb) + Pi(dr,r2,v_rel,rhoa,rhob,massb,visc));

					vd.getProp<force>(a)[0] += factor * DW.get(0);
					vd.getProp<force>(a)[1] += factor * DW.get(1);
					vd.getProp<force>(a)[2] += factor * DW.get(2);

					vd.getProp<drho>(a) += massb*(v_rel.get(0)*DW.get(0)+v_rel.get(1)*DW.get(1)+v_rel.get(2)*DW.get(2));
				}

				++Np;
			}
incardon's avatar
incardon committed
546
		}
incardon's avatar
incardon committed
547 548

		++part;
incardon's avatar
incardon committed
549
	}
incardon's avatar
incardon committed
550
}
incardon's avatar
incardon committed
551

incardon's avatar
incardon committed
552
/*! \cond [calc_forces] \endcond */
incardon's avatar
incardon committed
553

incardon's avatar
incardon committed
554 555 556 557 558 559 560 561 562 563
/*!
 *
 * \page Vector_7_sph_dlb Vector 7 SPH Dam break  simulation with Dynamic load balancing
 *
 * This function calculate the Maximum acceleration and velocity across the particles.
 *
 * \snippet Vector/7_SPH_dlb/main.cpp max_acc_vel
 *
 *
 */
incardon's avatar
incardon committed
564

incardon's avatar
incardon committed
565
/*! \cond [max_acc_vel] \endcond */
incardon's avatar
incardon committed
566 567 568 569 570 571 572 573 574 575 576 577 578 579 580 581 582 583 584 585 586 587 588 589 590 591 592 593

void max_acceleration_and_velocity(particles & vd, double & max_acc, double & max_vel)
{
	// Calculate the maximum acceleration
	auto part = vd.getDomainIterator();

	while (part.isNext())
	{
		auto a = part.get();

		Point<3,double> acc(vd.getProp<force>(a));
		double acc2 = norm2(acc);

		Point<3,double> vel(vd.getProp<velocity>(a));
		double vel2 = norm2(vel);

		if (vel2 >= max_vel)
			max_vel = vel2;

		if (acc2 >= max_acc)
			max_acc = acc2;

		++part;
	}
	max_acc = sqrt(max_acc);
	max_vel = sqrt(max_vel);
}

incardon's avatar
incardon committed
594 595 596 597 598 599 600 601 602 603 604 605 606 607 608 609 610 611 612 613 614 615 616 617
/*! \cond [max_acc_vel] \endcond */

/*!
 *
 * \page Vector_7_sph_dlb Vector 7 SPH Dam break  simulation with Dynamic load balancing
 *
 * In this example we are using Dynamic time-stepping. The Dynamic time stepping is
 * calculated with the Courant-Friedrich-Lewy condition. See Monaghan 1992 "Smoothed Particle Hydrodynamic"
 *
 * \f$ \delta t = CFL \cdot min(t_f,t_{cv}) \f$
 *
 * where
 *
 * \f$ \delta t_f = min \sqrt{h/f_a}\f$
 *
 * \f$  \delta t_{cv} = min \frac{h}{c_s + max \left| \frac{hv_{ab} \cdot r_{ab}}{r_{ab}^2} \right|} \f$
 *
 *
 * \snippet Vector/7_SPH_dlb/main.cpp dyn_stepping
 *
 *
 */

/*! \cond [dyn_stepping] \endcond */
incardon's avatar
incardon committed
618 619 620 621 622 623 624 625 626 627 628 629 630 631 632 633 634 635 636 637 638

double calc_deltaT(particles & vd, double ViscDtMax)
{
	double Maxacc = 0.0;
	double Maxvel = 0.0;
	max_acceleration_and_velocity(vd,Maxacc,Maxvel);

	//-dt1 depends on force per unit mass.
	const double dt_f = (Maxacc)?sqrt(H/Maxacc):std::numeric_limits<int>::max();

	//-dt2 combines the Courant and the viscous time-step controls.
	const double dt_cv = H/(std::max(cbar,Maxvel*10.) + H*ViscDtMax);

	//-dt new value of time step.
	double dt=double(CFLnumber)*std::min(dt_f,dt_cv);
	if(dt<double(DtMin))
		dt=double(DtMin);

	return dt;
}

incardon's avatar
incardon committed
639 640 641 642 643 644 645 646 647 648 649 650 651 652 653 654 655 656
/*! \cond [dyn_stepping] \endcond */

/*!
 *
 * \page Vector_7_sph_dlb Vector 7 SPH Dam break  simulation with Dynamic load balancing
 *
 * This function perform verlet integration accordingly to the Verlet time stepping scheme
 *
 * \f$ v_a^{n+1} = v_a^{n-1} + 2 \delta t F_a^{n} \f$
 *
 * \f$ r_a^{n+1} = \delta t V_a^n + 0.5 \delta t^2 F_a^n \f$
 *
 * \f$ \rho_a^{n+1} = \rho_a^{n-1} + 2 \delta t D_a^n \f$
 *
 * Every N Verlet steps the euler stepping scheme is choosen to avoid instabilities
 *
 * \f$ v_a^{n+1} = v_a^{n} + \delta t F_a^n \f$
 *
incardon's avatar
incardon committed
657
 * \f$ r_a^{n+1} = r_a^{n} + \delta t V_a^n + \frac{1}{2} \delta t^2 F_a^n \f$
incardon's avatar
incardon committed
658
 *
incardon's avatar
incardon committed
659
 * \f$ \rho_a^{n+1} = \rho_a^n + \delta t D_a^n \f$
incardon's avatar
incardon committed
660 661
 *
 * More the integration this function also check that no particles go outside the simulation
incardon's avatar
incardon committed
662 663
 * domain or their density go dangerously out of range. If a particle go out of range is removed
 * from the simulation
incardon's avatar
incardon committed
664 665 666 667 668 669 670 671
 *
 * \snippet Vector/7_SPH_dlb/main.cpp verlet_int
 *
 *
 */

/*! \cond [verlet_int] \endcond */

incardon's avatar
incardon committed
672 673
openfpm::vector<size_t> to_remove;

incardon's avatar
incardon committed
674
size_t cnt = 0;
incardon's avatar
incardon committed
675

incardon's avatar
incardon committed
676
void verlet_int(particles & vd, double dt, bool VerletStep)
incardon's avatar
incardon committed
677 678 679 680 681 682 683 684 685 686 687 688 689 690 691
{
	to_remove.clear();

	// Calculate the maximum acceleration
	auto part = vd.getDomainIterator();

	double dt205 = dt*dt*0.5;
	double dt2 = dt*2.0;

	while (part.isNext())
	{
		auto a = part.get();

		if (vd.template getProp<type>(a) == BOUNDARY)
		{
incardon's avatar
incardon committed
692 693
			double rhop = vd.template getProp<rho>(a);

incardon's avatar
incardon committed
694
			// Update only the density
incardon's avatar
incardon committed
695 696 697 698 699 700 701 702 703 704 705 706 707 708 709 710 711
		    if (VerletStep == true)
		    {
		    	vd.template getProp<velocity>(a)[0] = 0.0;
		    	vd.template getProp<velocity>(a)[1] = 0.0;
		    	vd.template getProp<velocity>(a)[2] = 0.0;
		    	vd.template getProp<rho>(a) = vd.template getProp<rho_prev>(a) + dt2*vd.template getProp<drho>(a);
		    }
		    else
		    {
		    	vd.template getProp<velocity>(a)[0] = 0.0;
		    	vd.template getProp<velocity>(a)[1] = 0.0;
		    	vd.template getProp<velocity>(a)[2] = 0.0;
		    	vd.template getProp<rho>(a) = vd.template getProp<rho>(a) + dt*vd.template getProp<drho>(a);
		    }

		    vd.template getProp<rho_prev>(a) = rhop;

incardon's avatar
incardon committed
712 713 714 715 716 717 718 719 720 721 722 723 724 725 726 727 728 729
			++part;
			continue;
		}

		//-Calculate displacement and update position / Calcula desplazamiento y actualiza posicion.
		double dx = vd.template getProp<velocity>(a)[0]*dt + vd.template getProp<force>(a)[0]*dt205;
	    double dy = vd.template getProp<velocity>(a)[1]*dt + vd.template getProp<force>(a)[1]*dt205;
	    double dz = vd.template getProp<velocity>(a)[2]*dt + vd.template getProp<force>(a)[2]*dt205;

	    vd.getPos(a)[0] += dx;
	    vd.getPos(a)[1] += dy;
	    vd.getPos(a)[2] += dz;

	    double velX = vd.template getProp<velocity>(a)[0];
	    double velY = vd.template getProp<velocity>(a)[1];
	    double velZ = vd.template getProp<velocity>(a)[2];
	    double rhop = vd.template getProp<rho>(a);

incardon's avatar
incardon committed
730 731 732 733 734 735 736 737 738 739 740 741 742 743 744 745 746 747 748 749 750 751 752
	    if (VerletStep == true)
	    {
	    	vd.template getProp<velocity>(a)[0] = vd.template getProp<velocity_prev>(a)[0] + vd.template getProp<force>(a)[0]*dt2;
	    	vd.template getProp<velocity>(a)[1] = vd.template getProp<velocity_prev>(a)[1] + vd.template getProp<force>(a)[1]*dt2;
	    	vd.template getProp<velocity>(a)[2] = vd.template getProp<velocity_prev>(a)[2] + vd.template getProp<force>(a)[2]*dt2;
	    	vd.template getProp<rho>(a) = vd.template getProp<rho_prev>(a) + dt2*vd.template getProp<drho>(a);
	    }
	    else
	    {
	    	vd.template getProp<velocity>(a)[0] = vd.template getProp<velocity>(a)[0] + vd.template getProp<force>(a)[0]*dt;
	    	vd.template getProp<velocity>(a)[1] = vd.template getProp<velocity>(a)[1] + vd.template getProp<force>(a)[1]*dt;
	    	vd.template getProp<velocity>(a)[2] = vd.template getProp<velocity>(a)[2] + vd.template getProp<force>(a)[2]*dt;
	    	vd.template getProp<rho>(a) = vd.template getProp<rho>(a) + dt*vd.template getProp<drho>(a);
	    }

	    // Check if there are particles to remove

	    if (vd.getPos(a)[0] <  0.000263878 || vd.getPos(a)[1] < 0.000263878 || vd.getPos(a)[2] < 0.000263878 ||
	        vd.getPos(a)[0] >  0.000263878+1.59947 || vd.getPos(a)[1] > 0.000263878+0.672972 || vd.getPos(a)[2] > 0.000263878+0.903944 ||
			vd.template getProp<rho>(a) < RhoMin || vd.template getProp<rho>(a) > RhoMax)
	    {
	                   to_remove.add(a.getKey());
	    }
incardon's avatar
incardon committed
753 754 755 756 757 758 759 760 761 762

	    vd.template getProp<velocity_prev>(a)[0] = velX;
	    vd.template getProp<velocity_prev>(a)[1] = velY;
	    vd.template getProp<velocity_prev>(a)[2] = velZ;
	    vd.template getProp<rho_prev>(a) = rhop;

		++part;
	}

	vd.remove(to_remove,0);
incardon's avatar
incardon committed
763 764

	cnt++;
incardon's avatar
incardon committed
765 766
}

incardon's avatar
incardon committed
767 768
/*! \cond [verlet_int] \endcond */

incardon's avatar
incardon committed
769 770 771 772
int main(int argc, char* argv[])
{
	/*!
	 *
incardon's avatar
incardon committed
773 774 775
	 * \page Vector_7_sph_dlb Vector 7 SPH Dam break  simulation with Dynamic load balancing
	 *
	 * ## Main function ##
incardon's avatar
incardon committed
776
	 *
incardon's avatar
incardon committed
777
	 * Here we Initialize the library, we create a Box that define our domain, boundary conditions and ghost
incardon's avatar
incardon committed
778 779 780 781 782 783 784 785 786 787 788 789 790
	 *
	 * \see \ref e0_s_init
	 *
	 * \snippet Vector/7_SPH_dlb/main.cpp Initialization and parameters
	 *
	 */

	//! \cond [Initialization and parameters] \endcond

    // initialize the library
	openfpm_init(&argc,&argv);

	// Here we define our domain a 2D box with internals from 0 to 1.0 for x and y
incardon's avatar
incardon committed
791 792
	Box<3,double> domain({-0.05,-0.05,-0.05},{1.7010,0.7065,0.5025});
	size_t sz[3] = {207,90,66};
incardon's avatar
incardon committed
793 794 795 796 797 798 799 800 801 802 803 804 805

	// Fill W_dap
	W_dap = 1.0/Wab(H/1.5);

	// Here we define the boundary conditions of our problem
    size_t bc[3]={NON_PERIODIC,NON_PERIODIC,NON_PERIODIC};

	// extended boundary around the domain, and the processor domain
	Ghost<3,double> g(2*H);
	
	//! \cond [Initialization and parameters] \endcond

	/*!
incardon's avatar
incardon committed
806
	 * \page Vector_7_sph_dlb Vector 7 SPH Dam break  simulation with Dynamic load balancing
incardon's avatar
incardon committed
807 808 809
	 *
	 * ## %Vector create ##
	 *
incardon's avatar
incardon committed
810 811 812 813 814 815 816 817 818 819 820
	 * Here we define a distributed vector in 3D, we use the particles type that we defined previously.
	 * Each particle contain the following properties const size_t type = 0;
	 * * **rho** Density of the particle;
 	 * * **rho_prev** Density at previous timestep
     * * **Pressure** Pressure of the particle
 	 * * **drho** Derivative of the density over time
	 * * **force** acceleration of the particles
	 * * **velocity** velocity of the particles
	 * * **velocity_prev** velocity of the particles at previous time-step
	 *
	 *
incardon's avatar
incardon committed
821 822 823 824
	 * In this case the vector contain 0 particles initially
	 *
	 * \see \ref vector_inst
	 *
incardon's avatar
incardon committed
825 826
	 * \snippet Vector/7_SPH_dlb/main.cpp vector inst
	 * \snippet Vector/7_SPH_dlb/main.cpp vector_dist_def
incardon's avatar
incardon committed
827 828 829 830 831
	 *
	 */

	//! \cond [vector inst] \endcond

incardon's avatar
incardon committed
832
	particles vd(0,domain,bc,g,DEC_GRAN(4096));
incardon's avatar
incardon committed
833 834 835

	//! \cond [vector inst] \endcond

incardon's avatar
incardon committed
836 837 838 839 840 841 842 843 844 845 846 847 848 849 850 851 852 853 854 855 856 857 858 859 860 861 862 863 864 865 866 867 868 869 870
	/*!
	 * \page Vector_7_sph_dlb Vector 7 SPH Dam break  simulation with Dynamic load balancing
	 *
	 * ## Draw particles and initialization ##
	 *
	 * In this part we initialize the problem creating particles in the position that
	 * we want. In order to do it we use the class DrawParticles. Because some of
	 * the simulation constants require the maximum height of the fluid to be calculated
	 *  and the maximum fluid height is determined at runtime, some of the constants are
	 *  calculated here. In this case the vector contain 0 particles initially.
	 *
	 *  ### Draw Fluid ###
	 *
	 *  We start drawing the fluid particles, the initial pressure is initialized accordingly to the
	 *  Hydrostatic pressure given by:
	 *
	 *  \f$ P = \rho_{0} g (h_{max} - z) \f$
	 *
	 * Where \f$ h_{max} \f$ is the maximum height of the fluid.
	 * The density instead is given by the equation (3). Assuming \f$ \rho \f$ constant to
	 * \f$ \rho_{0} \f$ in the Hydrostatic equation is a good approximation. Velocity is
	 * initialized to zero.
	 *
	 * \see \ref e0_s_vector_inst
	 *
	 * \htmlonly
	 * <img src="http://ppmcore.mpi-cbg.de/web/images/examples/7_SPH_dlb/fluid.jpg"/>
	 * \endhtmlonly
	 *
	 * \snippet Vector/7_SPH_dlb/main.cpp draw fluid
	 *
	 */

	//! \cond [draw fluid] \endcond

incardon's avatar
incardon committed
871 872 873
	// the scalar is the element at position 0 in the aggregate
	const int type = 0;

incardon's avatar
incardon committed
874
	Box<3,double> fluid_box({dp/2.0,dp/2.0,dp/2.0},{0.4+dp/2.0,0.67-dp/2.0,0.3+dp/2.0});
incardon's avatar
incardon committed
875 876 877 878 879

	// first we create Fluid particles
	// Fluid particles are created

	auto fluid_it = DrawParticles::DrawBox(vd,sz,domain,fluid_box);
incardon's avatar
incardon committed
880 881

	// here we fill some of the constants needed by the simulation
incardon's avatar
incardon committed
882 883 884 885 886 887 888 889 890 891 892 893 894 895 896 897 898 899 900 901 902 903 904 905 906 907 908 909 910 911 912 913 914 915 916 917 918
	max_fluid_height = fluid_it.getBoxMargins().getHigh(2);
	h_swl = fluid_it.getBoxMargins().getHigh(2) - fluid_it.getBoxMargins().getLow(2);
	B = (coeff_sound)*(coeff_sound)*gravity*h_swl*rho_zero / gamma_;
	cbar = coeff_sound * sqrt(gravity * h_swl);

	while (fluid_it.isNext())
	{
		vd.add();

		vd.getLastPos()[0] = fluid_it.get().get(0);
		vd.getLastPos()[1] = fluid_it.get().get(1);
		vd.getLastPos()[2] = fluid_it.get().get(2);

		vd.template getLastProp<type>() = FLUID;

		// We also initialize the density of the particle and the hydro-static pressure given by
		//
		// rho_zero*g*h = P
		//
		// rho_p = (P/B + 1)^(1/Gamma) * rho_zero
		//

		vd.template getLastProp<Pressure>() = rho_zero * gravity *  (max_fluid_height - fluid_it.get().get(2));

		vd.template getLastProp<rho>() = pow(vd.template getLastProp<Pressure>() / B + 1, 1.0/gamma_) * rho_zero;
		vd.template getLastProp<rho_prev>() = vd.template getLastProp<rho>();
		vd.template getLastProp<velocity>()[0] = 0.0;
		vd.template getLastProp<velocity>()[1] = 0.0;
		vd.template getLastProp<velocity>()[2] = 0.0;

		vd.template getLastProp<velocity_prev>()[0] = 0.0;
		vd.template getLastProp<velocity_prev>()[1] = 0.0;
		vd.template getLastProp<velocity_prev>()[2] = 0.0;

		++fluid_it;
	}

incardon's avatar
incardon committed
919 920 921 922 923 924 925 926 927 928 929 930 931 932 933 934 935 936 937 938 939 940 941 942 943 944 945
	//! \cond [draw fluid] \endcond

	/*!
	 * \page Vector_7_sph_dlb Vector 7 SPH Dam break  simulation with Dynamic load balancing
	 *
	 * ### Draw Recipient ###
	 *
	 * Here we draw the recipient using DrawSkin function. This function can draw a
	 * box of particles removed of a second box or an array of boxes. So all the particles in the area included
	 * in the shape A - B - C. There is no restriction that B or C must be included into A.
	 *
	 * \htmlonly
	 * <img src="http://ppmcore.mpi-cbg.de/web/images/examples/7_SPH_dlb/recipient.jpg"/>
	 * \endhtmlonly
	 *
	 * In this case A is the box defining the recipient, B is the box cutting out the internal
	 * part of the recipient, C is the hole where we will place the obstacle.
     * Because we use Dynamic boundary condition (DBC) we initialize the density
	 * to \f$ \rho_{0} \f$. It will be update over time according to equation (3) to keep
	 * the particles confined.
	 *
	 * \snippet Vector/7_SPH_dlb/main.cpp draw recipient
	 *
	 */

	//! \cond [draw recipient] \endcond

incardon's avatar
incardon committed
946 947 948 949 950 951 952 953 954 955 956 957 958 959 960 961 962 963 964 965 966 967 968 969 970 971 972 973 974 975 976 977 978 979 980
	// Recipient
	Box<3,double> recipient1({0.0,0.0,0.0},{1.6+dp/2.0,0.67+dp/2.0,0.4+dp/2.0});
	Box<3,double> recipient2({dp,dp,dp},{1.6-dp/2.0,0.67-dp/2.0,0.4+dp/2.0});

	Box<3,double> obstacle1({0.9,0.24-dp/2.0,0.0},{1.02+dp/2.0,0.36,0.45+dp/2.0});
	Box<3,double> obstacle2({0.9+dp,0.24+dp/2.0,0.0},{1.02-dp/2.0,0.36-dp,0.45-dp/2.0});
	Box<3,double> obstacle3({0.9+dp,0.24,0.0},{1.02,0.36,0.45});

	openfpm::vector<Box<3,double>> holes;
	holes.add(recipient2);
	holes.add(obstacle1);
	auto bound_box = DrawParticles::DrawSkin(vd,sz,domain,holes,recipient1);

	while (bound_box.isNext())
	{
		vd.add();

		vd.getLastPos()[0] = bound_box.get().get(0);
		vd.getLastPos()[1] = bound_box.get().get(1);
		vd.getLastPos()[2] = bound_box.get().get(2);

		vd.template getLastProp<type>() = BOUNDARY;
		vd.template getLastProp<rho>() = rho_zero;
		vd.template getLastProp<rho_prev>() = rho_zero;
		vd.template getLastProp<velocity>()[0] = 0.0;
		vd.template getLastProp<velocity>()[1] = 0.0;
		vd.template getLastProp<velocity>()[2] = 0.0;

		vd.template getLastProp<velocity_prev>()[0] = 0.0;
		vd.template getLastProp<velocity_prev>()[1] = 0.0;
		vd.template getLastProp<velocity_prev>()[2] = 0.0;

		++bound_box;
	}

incardon's avatar
incardon committed
981 982 983 984 985 986 987 988 989 990 991 992 993 994 995 996 997 998 999
	//! \cond [draw recipient] \endcond

	/*!
	 * \page Vector_7_sph_dlb Vector 7 SPH Dam break  simulation with Dynamic load balancing
	 *
	 *  ### Draw Obstacle ###
	 *
	 * Here we draw the obstacle in the same way we draw the recipient. also for the obstacle
	 * is valid the same concept of using Dynamic boundary condition (DBC)
	 *
	 * \htmlonly
	 * <img src="http://ppmcore.mpi-cbg.de/web/images/examples/7_SPH_dlb/obstacle.jpg"/>
	 * \endhtmlonly
	 *
	 * \snippet Vector/7_SPH_dlb/main.cpp draw obstacle
	 *
	 */

	//! \cond [draw obstacle] \endcond
incardon's avatar
incardon committed
1000 1001 1002 1003 1004 1005 1006 1007 1008 1009 1010 1011 1012 1013 1014 1015 1016 1017 1018 1019 1020 1021 1022 1023 1024 1025

	auto obstacle_box = DrawParticles::DrawSkin(vd,sz,domain,obstacle2,obstacle1);

	while (obstacle_box.isNext())
	{
		vd.add();

		vd.getLastPos()[0] = obstacle_box.get().get(0);
		vd.getLastPos()[1] = obstacle_box.get().get(1);
		vd.getLastPos()[2] = obstacle_box.get().get(2);

		vd.template getLastProp<type>() = BOUNDARY;
		vd.template getLastProp<rho>() = rho_zero;
		vd.template getLastProp<rho_prev>() = rho_zero;
		vd.template getLastProp<velocity>()[0] = 0.0;
		vd.template getLastProp<velocity>()[1] = 0.0;
		vd.template getLastProp<velocity>()[2] = 0.0;

		vd.template getLastProp<velocity_prev>()[0] = 0.0;
		vd.template getLastProp<velocity_prev>()[1] = 0.0;
		vd.template getLastProp<velocity_prev>()[2] = 0.0;

		++obstacle_box;
	}

	vd.map();
incardon's avatar
incardon committed
1026 1027 1028 1029 1030 1031 1032 1033 1034 1035 1036 1037 1038 1039 1040 1041 1042 1043 1044 1045 1046 1047 1048 1049 1050 1051 1052 1053 1054 1055 1056 1057 1058 1059 1060 1061 1062 1063 1064 1065 1066 1067 1068 1069 1070 1071 1072 1073 1074 1075 1076 1077 1078 1079 1080 1081 1082 1083 1084 1085 1086

	//! \cond [draw obstacle] \endcond

	/*!
	 * \page Vector_7_sph_dlb Vector 7 SPH Dam break  simulation with Dynamic load balancing
	 *
	 * ## Load balancing and Dynamic load balancing ##
	 *
	 * ### Load Balancing ###
	 *
	 * If at this point we output the particles and we visualize where they are accordingly
	 * to their processor id we can easily see that particles are distributed unevenly. The
	 * processor that has particle in while has few particles and all of them are non fluid.
	 * This mean that it will be almost in idle. This situation is not ideal
	 *
	 * \htmlonly
	 * <img src="http://ppmcore.mpi-cbg.de/web/images/examples/7_SPH_dlb/unbalanced_particles.jpg"/>
	 * \endhtmlonly
	 *
	 * In order to reach an optimal situation we have to distribute the particles in order to
	 * reach a balanced situation. In order to do this we have to set the computation of each
	 * sub-sub-domain, redecompose the space and distributed the particles accordingly to this
	 * new configuration. In order to do this we need a model. A model specify how to set
	 * the computational cost in each sub-subdomains (Quadratic, Linear, with the number of
	 * particles ...). In this special case where we have two type of particles, that different
	 * computational weight we use a custom model  in order to reach an optimal configuration.
	 * A custom model is nothing else than a structure with 3 methods.
	 *
	 * \snippet Vector/7_SPH_dlb/main.cpp model custom
	 *
	 * Setting the the computational cost on sub-domains is performed running across the particles.
	 * For each particles, it is calculated on which sub-sub-domain it belong. Than the function
	 * **addComputation** is called. Inside this call we can set the weight in the way we prefer.
	 * In this case we set the weight as:
	 *
	 * \f$ w_v =  \sum_{N_s} 3 N_{fluid} + 2N_{boundary} \f$
	 *
	 * Where \f$ N_{fluid} \f$ Is the number of fluid particles in the sub-sub-domain and \f$ N_{boundary} \f$
	 * are the number of boundary particles. While \f$ N_s = N_{fluid} + N_{boundary} \f$.
	 * This number is also used to calculate the cost in communication and in migration. The cost in communication
	 * is given by \f$ \frac{V_{ghost}}{V_{sub-sub}} w_v t_s \f$, while the migration cost is given by
	 * \f$ v_{sub-sub} w_v \f$. In general\f$ t_s \f$ is the number of ghost get between two rebalance.
	 * A second cycle is performed in order to calculate a complex function of this number (for example squaring).
	 * In our ModelCustom we square this number, because the computation is proportional to the square of the number
	 * of particles in each sub-sub-domain. After filled the computational cost based on out model
	 * we can decompose the problem in computational equal chunk for each processor. After
	 * we decomposed using the function **decompose()** we use the map function to redistribute
	 * the particles.
	 *
	 * \note All processors now has part of the fluid. It is good to note that the computationaly
	 *       balanced configuration does not correspond to the evenly distributed particles to know
	 *       more about that please follow the video tutorial
	 *
	 * \snippet Vector/7_SPH_dlb/main.cpp load balancing
	 *
	 * \htmlonly
	 * <img src="http://ppmcore.mpi-cbg.de/web/images/examples/7_SPH_dlb/load_balanced_particles.jpg"/>
	 * \endhtmlonly
	 *
	 */

incardon's avatar
incardon committed
1087
	vd.getDecomposition().write("Decomposition_before_load_bal");
incardon's avatar
incardon committed
1088 1089 1090
	vd.write("Geometry_before");

	//! \cond [load balancing] \endcond
incardon's avatar
incardon committed
1091 1092 1093 1094 1095

	// Now that we fill the vector with particles
	ModelCustom md;

	vd.addComputationCosts(md);
incardon's avatar
incardon committed
1096
	vd.getDecomposition().getDistribution().write("Distribution_BEFORE_DECOMPOSE");
incardon's avatar
incardon committed
1097 1098 1099
	vd.getDecomposition().decompose();
	vd.map();

incardon's avatar
incardon committed
1100
	//! \cond [load balancing] \endcond
incardon's avatar
incardon committed
1101

incardon's avatar
incardon committed
1102
	vd.addComputationCosts(md);
incardon's avatar
incardon committed
1103
//	vd.getDecomposition().getDistribution().write("AFTER_DECOMPOSE1");
incardon's avatar
incardon committed
1104

incardon's avatar
incardon committed
1105 1106 1107 1108
//	vd.getDecomposition().rebalance(1);

//	vd.map();
//	vd.getDecomposition().getDistribution().write("Distrobution_AFTER_DECOMPOSE");
incardon's avatar
incardon committed
1109 1110 1111

	std::cout << "N particles: " << vd.size_local()  << "    " << create_vcluster().getProcessUnitID() << "      " << "Get processor Load " << vd.getDecomposition().getDistribution().getProcessorLoad() << std::endl;

incardon's avatar
incardon committed
1112
	vd.write("Geometry_after");
incardon's avatar
incardon committed
1113 1114 1115 1116
	vd.getDecomposition().write("Decomposition_after_load_bal");
	vd.getDecomposition().getDistribution().write("Distribution_load_bal");

	vd.ghost_get<type,rho,Pressure,velocity>();
incardon's avatar
incardon committed
1117 1118 1119 1120 1121

	auto NN = vd.getCellList(2*H);

	// Evolve

incardon's avatar
incardon committed
1122 1123 1124 1125 1126 1127 1128 1129 1130 1131 1132 1133 1134 1135 1136
	/*!
	 * \page Vector_7_sph_dlb Vector 7 SPH Dam break  simulation with Dynamic load balancing
	 *
	 * ## Main Loop ##
	 *
	 * The main loop do time integration. It calculate the pressure based on the
	 * density, than calculate the forces, than we calculate delta time, and finally update position
	 * and velocity. After 200 time-step we do a rebalancing. And we save the configuration
	 * avery 0.01 seconds
	 *
	 * \snippet Vector/7_SPH_dlb/main.cpp main loop
	 *
	 */

	//! \cond [main loop] \endcond
incardon's avatar
incardon committed
1137

incardon's avatar
incardon committed
1138 1139 1140
	double time_mean = 0.0;
	double time_min = 1000.0;
	double time_max = 0.0;
incardon's avatar
incardon committed
1141 1142
	size_t write = 0;
	size_t it = 0;
incardon's avatar
incardon committed
1143
	size_t it_reb = 0;
incardon's avatar
incardon committed
1144 1145 1146
	double t = 0.0;
	while (t <= t_end)
	{
incardon's avatar
incardon committed
1147
		Vcluster & v_cl = create_vcluster();
incardon's avatar
incardon committed
1148 1149 1150 1151
		timer it_time;

		////// Do rebalancing every 200 timesteps
		it_reb++;
incardon's avatar
incardon committed
1152
		if (it_reb == 200)
incardon's avatar
incardon committed
1153 1154 1155
		{
			vd.map();

incardon's avatar
incardon committed
1156 1157
			vd.getDecomposition().write("DLB_BEFORE_");
//			it_reb = 0;
incardon's avatar
incardon committed
1158 1159
			ModelCustom md;
			vd.addComputationCosts(md);
incardon's avatar
incardon committed
1160
			vd.getDecomposition().decompose();
incardon's avatar
incardon committed
1161

incardon's avatar
incardon committed
1162 1163
			if (v_cl.getProcessUnitID() == 0)
				std::cout << "REBALANCED " << std::endl;
incardon's avatar
incardon committed
1164
		}
incardon's avatar
incardon committed
1165 1166

		vd.map();
incardon's avatar
incardon committed
1167 1168 1169 1170 1171 1172 1173 1174 1175 1176 1177 1178 1179 1180


		if (it_reb == 200)
		{
			vd.getDecomposition().write("DLB_AFTER_");

			it_reb = 0;
			vd.addComputationCosts(md);
			std::cout << "PROCESSOR LOAD: " << vd.getDecomposition().getDistribution().getProcessorLoad() << "   MEAN: " << time_mean / 200 << "     MIN: " << time_min << "      MAX: " << time_max  << std::endl;
			time_mean = 0.0;
			time_min = 1000.0;
			time_max = 0.0;
		}

incardon's avatar
incardon committed
1181
		vd.ghost_get<type,rho,Pressure,velocity>();
incardon's avatar
incardon committed
1182 1183 1184 1185 1186 1187

		// Calculate pressure from the density
		EqState(vd);

		double max_visc = 0.0;

incardon's avatar
incardon committed
1188 1189
		it_time.start();

incardon's avatar
incardon committed
1190 1191
		// Calc forces
		calc_forces(vd,NN,max_visc);
incardon's avatar
incardon committed
1192 1193 1194 1195 1196
		it_time.stop();

		// Get the maximum viscosity term across processors
		v_cl.max(max_visc);
		v_cl.execute();
incardon's avatar
incardon committed
1197 1198 1199
		time_mean += it_time.getwct();
		time_min = std::min(time_min,it_time.getwct());
		time_max = std::max(time_max,it_time.getwct());
incardon's avatar
incardon committed
1200 1201 1202 1203 1204 1205 1206

		// Calculate delta t integration
		double dt = calc_deltaT(vd,max_visc);

//		std::cout << "Calculate deltaT: " << dt << "   " << DtMin << std::endl;

		// VerletStep
incardon's avatar
incardon committed
1207 1208 1209 1210 1211 1212 1213 1214
		it++;
		if (it < 40)
			verlet_int(vd,dt,true);
		else
		{
			verlet_int(vd,dt,false);
			it = 0;
		}
incardon's avatar
incardon committed
1215 1216 1217 1218 1219 1220 1221 1222

		t += dt;

		if (write < t*100)
		{

			vd.write("Geometry",write);
			write++;
incardon's avatar
incardon committed
1223

incardon's avatar
incardon committed
1224 1225
			if (v_cl.getProcessUnitID() == 0)
				std::cout << "TIME: " << t << "  write " << it_time.getwct() << "   " << v_cl.getProcessUnitID() << "   " << cnt << std::endl;
incardon's avatar
incardon committed
1226 1227 1228
		}
		else
		{
incardon's avatar
incardon committed
1229 1230
			if (v_cl.getProcessUnitID() == 0)
				std::cout << "TIME: " << t << "  " << it_time.getwct() << "   " << v_cl.getProcessUnitID() << "   " << cnt << std::endl;
incardon's avatar
incardon committed
1231 1232 1233
		}
	}

incardon's avatar
incardon committed
1234 1235 1236 1237 1238 1239 1240 1241 1242 1243 1244 1245 1246 1247 1248
	//! \cond [main loop] \endcond

	/*!
	 *
	 * \page Vector_7_sph_dlb Vector 7 SPH Dam break  simulation with Dynamic load balancing
	 *
	 * ## Finalize ## {#finalize_e0_sim}
	 *
	 *
	 *  At the very end of the program we have always de-initialize the library
	 *
	 * \snippet Vector/7_SPH_dlb/main.cpp finalize
	 *
	 */

incardon's avatar
incardon committed
1249 1250 1251 1252 1253 1254 1255
	//! \cond [finalize] \endcond

	openfpm_finalize();

	//! \cond [finalize] \endcond

	/*!
incardon's avatar
incardon committed
1256
	 * \page Vector_7_sph_dlb Vector 7 SPH Dam break  simulation with Dynamic load balancing
incardon's avatar
incardon committed
1257
	 *
incardon's avatar
incardon committed
1258
	 * ## Full code ## {#code_e7_sph_dlb}
incardon's avatar
incardon committed
1259
	 *
incardon's avatar
incardon committed
1260
	 * \include Vector/7_SPH_dlb/main.cpp
incardon's avatar
incardon committed
1261 1262 1263 1264
	 *
	 */
}