diff --git a/src/FiniteDifference/Eno_Weno.hpp b/src/FiniteDifference/Eno_Weno.hpp new file mode 100644 index 0000000000000000000000000000000000000000..dc2bf99a0d40e597643f09971e0bfe8364760adb --- /dev/null +++ b/src/FiniteDifference/Eno_Weno.hpp @@ -0,0 +1,153 @@ +/* + * + * Based on the description in Osher and Fedkiw, Level Set Methods and Dynamic Implicit Surfaces + * For HJ ENO method - Sec. 3.3 + * For HJ WENO method - Sec. 3.4 +*/ + +#ifndef __ENO_WENO_HPP__ +#define __ENO_WENO_HPP__ + +#include "Grid/grid_dist_id.hpp" + +double adjustWeights(double v1, double v2, double v3, double v4, double v5) +{ + double phix1, phix2, phix3; + double s1, s2, s3; + double a1, a2, a3; + double eps = 1e-6; + double w1, w2, w3; + + // Eqs. (3.25), (3.26), (3.27) + phix1 = (v1 / 3.0) - (7.0 * v2 / 6.0) + (11.0 * v3 / 6.0); + phix2 = -(v2 / 6.0) + (5.0 * v3 / 6.0) + (v4 / 3.0); + phix3 = (v3 / 3.0) + (5.0 * v4 / 6.0) - (v5 / 6.0); + + // Eqs. (3.32), (3.33), (3.34) + s1 = (13.0 / 12.0) * (v1 - 2*v2 + v3) * (v1 - 2*v2 + v3) + + 0.25 * (v1 - 4*v2 + 3*v3) * (v1 - 4*v2 + 3*v3); + s2 = (13.0 / 12.0) * (v2 - 2*v3 + v4) * (v2 - 2*v3 + v4) + + 0.25 * (v2 - v4) * (v2 - v4); + s3 = (13.0 / 12.0) * (v3 - 2*v4 + v5) * (v3 - 2*v4 + v5) + + 0.25 * (3*v3 - 4*v4 + v5) * (3*v3 - 4*v4 + v5); + + // Eqs. (3.35), (3.36), (3.37) + a1 = 0.1 / ((s1 + eps)*(s1 + eps)); + a2 = 0.6 / ((s2 + eps)*(s2 + eps)); + a3 = 0.3 / ((s3 + eps)*(s3 + eps)); + + // Eqs. (3.39), (3.40), (3.41) + w1 = a1 / (a1 + a2 + a3); + w2 = a2 / (a1 + a2 + a3); + w3 = a3 / (a1 + a2 + a3); + + // Eq. (3.28) + return (w1 * phix1 + w2 * phix2 + w3 * phix3); +} + +template<typename GridDist, typename GridKey, unsigned int field, unsigned int x> +double WENO_5_Plus(GridKey key, GridDist &gd) +{ + double c2, c3, c4, c5, c6; + double coeff = 1.0 / gd.spacing(x); + double df; + + c2 = (gd.template get<field>(key.move(x, -1)) - gd.template get<field>(key.move(x, -2))) * coeff; + c3 = (gd.template get<field>(key) - gd.template get<field>(key.move(x, -1))) * coeff; + c4 = (gd.template get<field>(key.move(x,1)) - gd.template get<field>(key)) * coeff; + c5 = (gd.template get<field>(key.move(x, 2)) - gd.template get<field>(key.move(x, 1))) * coeff; + c6 = (gd.template get<field>(key.move(x, 3)) - gd.template get<field>(key.move(x, 2))) * coeff; + df = adjustWeights(c6, c5, c4, c3, c2); + + return df; +} + +template<typename GridDist, typename GridKey, unsigned int field, unsigned int x> +double WENO_5_Minus(GridKey key, GridDist &gd) +{ + double c1, c2, c3, c4, c5; + double coeff = 1.0 / gd.spacing(x); + double df; + + c1 = (gd.template get<field>(key.move(x, -2)) - gd.template get<field>(key.move(x, -3))) * coeff; + c2 = (gd.template get<field>(key.move(x, -1)) - gd.template get<field>(key.move(x, -2))) * coeff; + c3 = (gd.template get<field>(key) - gd.template get<field>(key.move(x, -1))) * coeff; + c4 = (gd.template get<field>(key.move(x,1)) - gd.template get<field>(key)) * coeff; + c5 = (gd.template get<field>(key.move(x, 2)) - gd.template get<field>(key.move(x, 1))) * coeff; + + df = adjustWeights(c1, c2, c3, c4, c5); + + return df; +} + +template<typename GridDist, typename GridKey, unsigned int field, unsigned int x> +double ENO_3_Plus(GridKey key, GridDist &gd) +{ + double q1x, q2x, q3x; + double gridsize = gd.spacing(x); + double coeff = 1.0 / gridsize; + + q1x = (gd.template get<field>(key.move(x,1)) - gd.template get<field>(key)) * coeff; + double d2ix = (gd.template get<field>(key.move(x,1)) - 2*gd.template get<field>(key) + gd.template get<field>(key.move(x,-1))) * 0.5 * coeff * coeff; + double d2ip1x = (gd.template get<field>(key.move(x,2)) - 2*gd.template get<field>(key.move(x,1)) + gd.template get<field>(key)) * 0.5 * coeff * coeff; + if(abs(d2ix) <= abs(d2ip1x)) + { + q2x = -d2ix * gridsize; + double d3p1hx = (gd.template get<field>(key.move(x,1)) - 3*gd.template get<field>(key) + 3*gd.template get<field>(key.move(x,-1)) - gd.template get<field>(key.move(x,-2))) * coeff * coeff * coeff / 6.0; + double d3p3hx = (gd.template get<field>(key.move(x,2)) - 3*gd.template get<field>(key.move(x,1)) + 3*gd.template get<field>(key) - gd.template get<field>(key.move(x,-1))) * coeff * coeff * coeff / 6.0; + if(abs(d3p1hx) <= abs(d3p3hx)) + q3x = -d3p1hx * gridsize * gridsize; + else + q3x = -d3p3hx * gridsize * gridsize; + } + else + { + q2x = -d2ip1x * gridsize; + double d3p1hx = (gd.template get<field>(key.move(x,2)) - 3*gd.template get<field>(key.move(x,1)) + 3*gd.template get<field>(key) - gd.template get<field>(key.move(x,-1))) * coeff * coeff * coeff / 6.0; + double d3p3hx = (gd.template get<field>(key.move(x,3)) - 3*gd.template get<field>(key.move(x,2)) + 3*gd.template get<field>(key.move(x,1)) - gd.template get<field>(key)) * coeff * coeff * coeff / 6.0; + if(abs(d3p1hx) <= abs(d3p3hx)) + q3x = d3p1hx * 2 * gridsize * gridsize; + else + q3x = d3p3hx * 2 * gridsize * gridsize; + + } + return (q1x + q2x + q3x); +} + +template<typename GridDist, typename GridKey, unsigned int field, unsigned int x> +double ENO_3_Minus(GridKey key, GridDist &gd) +{ + double q1x, q2x, q3x; + double gridsize = gd.spacing(x); + double coeff = 1.0 / gridsize; + + q1x = (gd.template get<field>(key) - gd.template get<field>(key.move(x, -1))) * coeff; + double d2im1x = (gd.template get<field>(key) - 2*gd.template get<field>(key.move(x, -1)) + gd.template get<field>(key.move(x, -2))) * 0.5 * coeff * coeff; + double d2ix = (gd.template get<field>(key.move(x,1)) - 2*gd.template get<field>(key) + gd.template get<field>(key.move(x,-1))) * 0.5 * coeff * coeff; + + if(abs(d2im1x) <= abs(d2ix)) + { + q2x = d2im1x * gridsize; + double d3p1hx = (gd.template get<field>(key) - 3*gd.template get<field>(key.move(x,-1)) + 3*gd.template get<field>(key.move(x,-2)) - gd.template get<field>(key.move(x,-3))) * coeff * coeff * coeff / 6.0; + double d3p3hx = (gd.template get<field>(key.move(x,1)) - 3*gd.template get<field>(key) + 3*gd.template get<field>(key.move(x,-1)) - gd.template get<field>(key.move(x,-2))) * coeff * coeff * coeff / 6.0; + if(abs(d3p1hx) <= abs(d3p3hx)) + q3x = d3p1hx * 2 * gridsize * gridsize; + else + q3x = d3p3hx * 2 * gridsize * gridsize; + } + else + { + q2x = d2ix * gridsize; + double d3p1hx = (gd.template get<field>(key.move(x,1)) - 3*gd.template get<field>(key) + 3*gd.template get<field>(key.move(x,-1)) - gd.template get<field>(key.move(x,-2))) * coeff * coeff * coeff / 6.0; + double d3p3hx = (gd.template get<field>(key.move(x,2)) - 3*gd.template get<field>(key.move(x,1)) + 3*gd.template get<field>(key) - gd.template get<field>(key.move(x,-1))) * coeff * coeff * coeff / 6.0; + if(abs(d3p1hx) <= abs(d3p3hx)) + q3x = -d3p1hx * gridsize * gridsize; + else + q3x = -d3p3hx * gridsize * gridsize; + } + + return (q1x + q2x + q3x); +} + +#endif +