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Derivative.hpp 13.70 KiB
/*
* Derivative.hpp
*
* Created on: Oct 5, 2015
* Author: Pietro Incardona
*/
#ifndef OPENFPM_NUMERICS_SRC_FINITEDIFFERENCE_DERIVATIVE_HPP_
#define OPENFPM_NUMERICS_SRC_FINITEDIFFERENCE_DERIVATIVE_HPP_
#include "util/mathutil.hpp"
#include "Vector/map_vector.hpp"
#include "Grid/comb.hpp"
#include "FiniteDifference/util/common.hpp"
#include "util/util_num.hpp"
#include <unordered_map>
#include "FD_util_include.hpp"
/*! \brief Derivative second order on h (spacing)
*
* \tparam d on which dimension derive
* \tparam Field which field derive
* \tparam impl which implementation
*
*/
template<unsigned int d, typename Field, typename Sys_eqs, unsigned int impl=CENTRAL>
class D
{
/*! \brief Calculate which colums of the Matrix are non zero
*
* \param pos position where the derivative is calculated
* \param gs Grid info
* \param cols non-zero colums calculated by the function
* \param coeff coefficent (constant in front of the derivative)
*
* ### Example
*
* \snippet FDScheme_unit_tests.hpp Usage of stencil derivative
*
*/
inline static void value(const grid_key_dx<Sys_eqs::dims> & pos, const grid_sm<Sys_eqs::dims,void> & gs, std::unordered_map<long int,typename Sys_eqs::stype > & cols, typename Sys_eqs::stype coeff)
{
std::cerr << "Error " << __FILE__ << ":" << __LINE__ << " only CENTRAL, FORWARD, BACKWARD derivative are defined";
}
/*! \brief Calculate the position where the derivative is calculated
*
* In case of non staggered case this function just return a null grid_key, in case of staggered,
* it calculate how the operator shift the calculation in the cell
*
* \param pos position where we are calculating the derivative
* \param gs Grid info
* \param s_pos staggered position of the properties
*
* \return where (in which cell) the derivative is calculated
*
*/
inline static grid_key_dx<Sys_eqs::dims> position(grid_key_dx<Sys_eqs::dims> & pos,
const grid_sm<Sys_eqs::dims,void> & gs,
const comb<Sys_eqs::dims> (& s_pos)[Sys_eqs::nvar])
{
std::cerr << "Error " << __FILE__ << ":" << __LINE__ << " only CENTRAL, FORWARD, BACKWARD derivative are defined";
return pos;
}
};
/*! \brief Second order central Derivative scheme on direction i
* * \verbatim
*
* -1 +1
* *---+---*
*
* \endverbatim
*
*/
template<unsigned int d, typename arg, typename Sys_eqs>
class D<d,arg,Sys_eqs,CENTRAL>
{
public:
/*! \brief Calculate which colums of the Matrix are non zero
*
* \param g_map mapping grid
* \param kmap position where the derivative is calculated
* \param gs Grid info
* \param spacing grid spacing
* \param cols non-zero colums calculated by the function
* \param coeff coefficent (constant in front of the derivative)
*
* ### Example
*
* \snippet FDScheme_unit_tests.hpp Usage of stencil derivative
*
*/
inline static void value(const typename stub_or_real<Sys_eqs,Sys_eqs::dims,typename Sys_eqs::stype,typename Sys_eqs::b_grid::decomposition::extended_type>::type & g_map,
grid_dist_key_dx<Sys_eqs::dims> & kmap,
const grid_sm<Sys_eqs::dims,void> & gs,
typename Sys_eqs::stype (& spacing )[Sys_eqs::dims],
std::unordered_map<long int,typename Sys_eqs::stype > & cols,
typename Sys_eqs::stype coeff)
{
// if the system is staggered the CENTRAL derivative is equivalent to a forward derivative
if (is_grid_staggered<Sys_eqs>::value())
{
D<d,arg,Sys_eqs,BACKWARD>::value(g_map,kmap,gs,spacing,cols,coeff);
return;
}
long int old_val = kmap.getKeyRef().get(d);
kmap.getKeyRef().set_d(d, kmap.getKeyRef().get(d) + 1);
arg::value(g_map,kmap,gs,spacing,cols,coeff/spacing[d]/2.0 );
kmap.getKeyRef().set_d(d,old_val);
old_val = kmap.getKeyRef().get(d);
kmap.getKeyRef().set_d(d, kmap.getKeyRef().get(d) - 1);
arg::value(g_map,kmap,gs,spacing,cols,-coeff/spacing[d]/2.0 );
kmap.getKeyRef().set_d(d,old_val);
}
/*! \brief Calculate the position where the derivative is calculated
*
* In case on non staggered case this function just return a null grid_key, in case of staggered,
* it calculate how the operator shift in the cell
*
\verbatim
+--$--+
| |
# * #
| |
0--$--+
# = velocity(y)
$ = velocity(x)
* = pressure
\endverbatim
*
* Consider this 2D staggered cell and a second order central derivative scheme, this lead to
*
* \f$ \frac{\partial v_y}{\partial x} \f$ is calculated on position (*), so the function return the grid_key {0,0}
*
* \f$ \frac{\partial v_y}{\partial y} \f$ is calculated on position (0), so the function return the grid_key {-1,-1}
*
* \f$ \frac{\partial v_x}{\partial x} \f$ is calculated on position (0), so the function return the grid_key {-1,-1}
*
* \f$ \frac{\partial v_x}{\partial y} \f$ is calculated on position (*), so the function return the grid_key {0,0}
*
* \param pos position where we are calculating the derivative
* \param gs Grid info
* \param s_pos staggered position of the properties
*
* \return where (in which cell grid) the derivative is calculated
*
*/
inline static grid_key_dx<Sys_eqs::dims> position(grid_key_dx<Sys_eqs::dims> & pos,
const grid_sm<Sys_eqs::dims,void> & gs,
const comb<Sys_eqs::dims> (& s_pos)[Sys_eqs::nvar])
{
auto arg_pos = arg::position(pos,gs,s_pos);
if (is_grid_staggered<Sys_eqs>::value())
{
if (arg_pos.get(d) == -1)
{
arg_pos.set_d(d,0);
return arg_pos;
}
else
{
arg_pos.set_d(d,-1);
return arg_pos;
}
}
return arg_pos;
}
};
/*! \brief Second order one sided Derivative scheme on direction i
*
* \verbatim
*
* -1.5 2.0 -0.5
* +------*------*
*
* or
*
* -0.5 2.0 -1.5
* *------*------+
*
* in the bulk
*
* -1 +1
* *---+---*
*
* \endverbatim
*
*/
template<unsigned int d, typename arg, typename Sys_eqs>
class D<d,arg,Sys_eqs,CENTRAL_B_ONE_SIDE>
{
public:
/*! \brief Calculate which colums of the Matrix are non zero *
* \param g_map mapping grid points
* \param kmap position where the derivative is calculated
* \param gs Grid info
* \param spacing of the grid
* \param cols non-zero colums calculated by the function
* \param coeff coefficent (constant in front of the derivative)
*
* ### Example
*
* \snippet FDScheme_unit_tests.hpp Usage of stencil derivative
*
*/
static void value(const typename stub_or_real<Sys_eqs,Sys_eqs::dims,typename Sys_eqs::stype,typename Sys_eqs::b_grid::decomposition::extended_type>::type & g_map,
grid_dist_key_dx<Sys_eqs::dims> & kmap,
const grid_sm<Sys_eqs::dims,void> & gs,
typename Sys_eqs::stype (& spacing )[Sys_eqs::dims],
std::unordered_map<long int,typename Sys_eqs::stype > & cols,
typename Sys_eqs::stype coeff)
{
#ifdef SE_CLASS1
if (Sys_eqs::boundary[d] == PERIODIC)
std::cerr << __FILE__ << ":" << __LINE__ << " error, it make no sense use one sided derivation with periodic boundary, please use CENTRAL\n";
#endif
grid_key_dx<Sys_eqs::dims> pos = g_map.getGKey(kmap);
if (pos.get(d) == (long int)gs.size(d)-1 )
{
arg::value(g_map,kmap,gs,spacing,cols,1.5*coeff/spacing[d]);
long int old_val = kmap.getKeyRef().get(d);
kmap.getKeyRef().set_d(d, kmap.getKeyRef().get(d) - 1);
arg::value(g_map,kmap,gs,spacing,cols,-2.0*coeff/spacing[d]);
kmap.getKeyRef().set_d(d,old_val);
old_val = kmap.getKeyRef().get(d);
kmap.getKeyRef().set_d(d, kmap.getKeyRef().get(d) - 2);
arg::value(g_map,kmap,gs,spacing,cols,0.5*coeff/spacing[d]);
kmap.getKeyRef().set_d(d,old_val);
}
else if (pos.get(d) == 0)
{
arg::value(g_map,kmap,gs,spacing,cols,-1.5*coeff/spacing[d]);
long int old_val = kmap.getKeyRef().get(d);
kmap.getKeyRef().set_d(d, kmap.getKeyRef().get(d) + 1);
arg::value(g_map,kmap,gs,spacing,cols,2.0*coeff/spacing[d]);
kmap.getKeyRef().set_d(d,old_val);
old_val = kmap.getKeyRef().get(d);
kmap.getKeyRef().set_d(d, kmap.getKeyRef().get(d) + 2);
arg::value(g_map,kmap,gs,spacing,cols,-0.5*coeff/spacing[d]);
kmap.getKeyRef().set_d(d,old_val);
}
else
{
long int old_val = kmap.getKeyRef().get(d);
kmap.getKeyRef().set_d(d, kmap.getKeyRef().get(d) + 1);
arg::value(g_map,kmap,gs,spacing,cols,coeff/spacing[d]);
kmap.getKeyRef().set_d(d,old_val);
old_val = kmap.getKeyRef().get(d);
kmap.getKeyRef().set_d(d, kmap.getKeyRef().get(d) - 1);
arg::value(g_map,kmap,gs,spacing,cols,-coeff/spacing[d]);
kmap.getKeyRef().set_d(d,old_val);
}
}
/*! \brief Calculate the position where the derivative is calculated *
* In case on non staggered case this function just return a null grid_key, in case of staggered,
* it calculate how the operator shift in the cell
*
\verbatim
+--$--+
| |
# * #
| |
0--$--+
# = velocity(y)
$ = velocity(x)
* = pressure
\endverbatim
*
* In the one side stencil the cell position depend if you are or not at the boundary.
* outside the boundary is simply the central scheme, at the boundary it is simply the
* staggered position of the property
*
* \param pos position where we are calculating the derivative
* \param gs Grid info
* \param s_pos staggered position of the properties
*
* \return where (in which cell grid) the derivative is calculated
*
*/
inline static grid_key_dx<Sys_eqs::dims> position(grid_key_dx<Sys_eqs::dims> & pos, const grid_sm<Sys_eqs::dims,void> & gs, const comb<Sys_eqs::dims> (& s_pos)[Sys_eqs::nvar])
{
return arg::position(pos,gs,s_pos);
}
};
/*! \brief First order FORWARD derivative on direction i
*
* \verbatim
*
* -1.0 1.0
* +------*
*
* \endverbatim
*
*/
template<unsigned int d, typename arg, typename Sys_eqs>
class D<d,arg,Sys_eqs,FORWARD>
{
public:
/*! \brief Calculate which colums of the Matrix are non zero
*
* \param g_map mapping grid
* \param kmap position where the derivative is calculated
* \param gs Grid info
* \param spacing grid spacing
* \param cols non-zero colums calculated by the function
* \param coeff coefficent (constant in front of the derivative)
*
* ### Example
*
* \snippet FDScheme_unit_tests.hpp Usage of stencil derivative
*
*/
inline static void value(const typename stub_or_real<Sys_eqs,Sys_eqs::dims,typename Sys_eqs::stype,typename Sys_eqs::b_grid::decomposition::extended_type>::type & g_map,
grid_dist_key_dx<Sys_eqs::dims> & kmap,
const grid_sm<Sys_eqs::dims,void> & gs,
typename Sys_eqs::stype (& spacing )[Sys_eqs::dims],
std::unordered_map<long int,typename Sys_eqs::stype > & cols, typename Sys_eqs::stype coeff)
{
long int old_val = kmap.getKeyRef().get(d);
kmap.getKeyRef().set_d(d, kmap.getKeyRef().get(d) + 1);
arg::value(g_map,kmap,gs,spacing,cols,coeff/spacing[d]);
kmap.getKeyRef().set_d(d,old_val);
// backward
arg::value(g_map,kmap,gs,spacing,cols,-coeff/spacing[d]);
}
/*! \brief Calculate the position where the derivative is calculated
*
* In case of non staggered case this function just return a null grid_key, in case of staggered,
* the FORWARD scheme return the position of the staggered property
*
* \param pos position where we are calculating the derivative
* \param gs Grid info
* \param s_pos staggered position of the properties
*
* \return where (in which cell grid) the derivative is calculated
*
*/
inline static grid_key_dx<Sys_eqs::dims> position(grid_key_dx<Sys_eqs::dims> & pos,
const grid_sm<Sys_eqs::dims,void> & gs,
const comb<Sys_eqs::dims> (& s_pos)[Sys_eqs::nvar])
{
return arg::position(pos,gs,s_pos);
}
};
/*! \brief First order BACKWARD derivative on direction i
*
* \verbatim
*
* -1.0 1.0
* *------+
*
* \endverbatim
*
*/
template<unsigned int d, typename arg, typename Sys_eqs>
class D<d,arg,Sys_eqs,BACKWARD>
{
public:
/*! \brief Calculate which colums of the Matrix are non zero
*
* \param g_map mapping grid
* \param kmap position where the derivative is calculated
* \param gs Grid info
* \param spacing of the grid
* \param cols non-zero colums calculated by the function
* \param coeff coefficent (constant in front of the derivative)
*
* ### Example
*
* \snippet FDScheme_unit_tests.hpp Usage of stencil derivative
*
*/
inline static void value(const typename stub_or_real<Sys_eqs,Sys_eqs::dims,typename Sys_eqs::stype,typename Sys_eqs::b_grid::decomposition::extended_type>::type & g_map,
grid_dist_key_dx<Sys_eqs::dims> & kmap,
const grid_sm<Sys_eqs::dims,void> & gs,
typename Sys_eqs::stype (& spacing )[Sys_eqs::dims],
std::unordered_map<long int,typename Sys_eqs::stype > & cols,
typename Sys_eqs::stype coeff)
{
long int old_val = kmap.getKeyRef().get(d);
kmap.getKeyRef().set_d(d, kmap.getKeyRef().get(d) - 1);
arg::value(g_map,kmap,gs,spacing,cols,-coeff/spacing[d]);
kmap.getKeyRef().set_d(d,old_val);
// forward
arg::value(g_map,kmap,gs,spacing,cols,coeff/spacing[d]);
}
/*! \brief Calculate the position where the derivative is calculated
*
* In case of non staggered case this function just return a null grid_key, in case of staggered,
* the BACKWARD scheme return the position of the staggered property
*
* \param pos position where we are calculating the derivative
* \param gs Grid info
* \param s_pos staggered position of the properties
*
* \return where (in which cell grid) the derivative is calculated
*
*/
inline static grid_key_dx<Sys_eqs::dims> position(grid_key_dx<Sys_eqs::dims> & pos, const grid_sm<Sys_eqs::dims,void> & gs, const comb<Sys_eqs::dims> (& s_pos)[Sys_eqs::nvar])
{
return arg::position(pos,gs,s_pos);
}
};
#endif /* OPENFPM_NUMERICS_SRC_FINITEDIFFERENCE_DERIVATIVE_HPP_ */