# src/viscosity.h

 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 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 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185  #include "poisson.h" struct Viscosity { vector u; face vector mu; scalar rho; double dt; int nrelax; scalar * res; }; #if AXI # define lambda ((coord){1., 1. + dt/rho[]*(mu.x[] + mu.x[1] + \ mu.y[] + mu.y[0,1])/2./sq(y)}) #else // not AXI # if dimension == 1 # define lambda ((coord){1.}) # elif dimension == 2 # define lambda ((coord){1.,1.}) # elif dimension == 3 # define lambda ((coord){1.,1.,1.}) #endif #endif static void relax_viscosity (scalar * a, scalar * b, int l, void * data) { struct Viscosity * p = (struct Viscosity *) data; (const) face vector mu = p->mu; (const) scalar rho = p->rho; double dt = p->dt; vector u = vector(a[0]), r = vector(b[0]); #if JACOBI vector w[]; #else vector w = u; #endif foreach_level_or_leaf (l) { foreach_dimension() w.x[] = (dt/rho[]*(2.*mu.x[1]*u.x[1] + 2.*mu.x[]*u.x[-1] #if dimension > 1 + mu.y[0,1]*(u.x[0,1] + (u.y[1,0] + u.y[1,1])/4. - (u.y[-1,0] + u.y[-1,1])/4.) - mu.y[]*(- u.x[0,-1] + (u.y[1,-1] + u.y[1,0])/4. - (u.y[-1,-1] + u.y[-1,0])/4.) #endif #if dimension > 2 + mu.z[0,0,1]*(u.x[0,0,1] + (u.z[1,0,0] + u.z[1,0,1])/4. - (u.z[-1,0,0] + u.z[-1,0,1])/4.) - mu.z[]*(- u.x[0,0,-1] + (u.z[1,0,-1] + u.z[1,0,0])/4. - (u.z[-1,0,-1] + u.z[-1,0,0])/4.) #endif ) + r.x[]*sq(Delta))/ (sq(Delta)*lambda.x + dt/rho[]*(2.*mu.x[1] + 2.*mu.x[] #if dimension > 1 + mu.y[0,1] + mu.y[] #endif #if dimension > 2 + mu.z[0,0,1] + mu.z[] #endif )); } #if JACOBI foreach_level_or_leaf (l) foreach_dimension() u.x[] = (u.x[] + 2.*w.x[])/3.; #endif #if TRASH vector u1[]; foreach_level_or_leaf (l) foreach_dimension() u1.x[] = u.x[]; trash ({u}); foreach_level_or_leaf (l) foreach_dimension() u.x[] = u1.x[]; #endif } static double residual_viscosity (scalar * a, scalar * b, scalar * resl, void * data) { struct Viscosity * p = (struct Viscosity *) data; (const) face vector mu = p->mu; (const) scalar rho = p->rho; double dt = p->dt; vector u = vector(a[0]), r = vector(b[0]), res = vector(resl[0]); double maxres = 0.; #if TREE /* conservative coarse/fine discretisation (2nd order) */ foreach_dimension() { face vector taux[]; foreach_face(x) taux.x[] = 2.*mu.x[]*(u.x[] - u.x[-1])/Delta; #if dimension > 1 foreach_face(y) taux.y[] = mu.y[]*(u.x[] - u.x[0,-1] + (u.y[1,-1] + u.y[1,0])/4. - (u.y[-1,-1] + u.y[-1,0])/4.)/Delta; #endif #if dimension > 2 foreach_face(z) taux.z[] = mu.z[]*(u.x[] - u.x[0,0,-1] + (u.z[1,0,-1] + u.z[1,0,0])/4. - (u.z[-1,0,-1] + u.z[-1,0,0])/4.)/Delta; #endif boundary_flux ({taux}); foreach (reduction(max:maxres)) { double d = 0.; foreach_dimension() d += taux.x[1] - taux.x[]; res.x[] = r.x[] - lambda.x*u.x[] + dt/rho[]*d/Delta; if (fabs (res.x[]) > maxres) maxres = fabs (res.x[]); } } boundary (resl); #else /* "naive" discretisation (only 1st order on trees) */ foreach (reduction(max:maxres)) foreach_dimension() { res.x[] = r.x[] - lambda.x*u.x[] + dt/rho[]*(2.*mu.x[1,0]*(u.x[1] - u.x[]) - 2.*mu.x[]*(u.x[] - u.x[-1]) #if dimension > 1 + mu.y[0,1]*(u.x[0,1] - u.x[] + (u.y[1,0] + u.y[1,1])/4. - (u.y[-1,0] + u.y[-1,1])/4.) - mu.y[]*(u.x[] - u.x[0,-1] + (u.y[1,-1] + u.y[1,0])/4. - (u.y[-1,-1] + u.y[-1,0])/4.) #endif #if dimension > 2 + mu.z[0,0,1]*(u.x[0,0,1] - u.x[] + (u.z[1,0,0] + u.z[1,0,1])/4. - (u.z[-1,0,0] + u.z[-1,0,1])/4.) - mu.z[]*(u.x[] - u.x[0,0,-1] + (u.z[1,0,-1] + u.z[1,0,0])/4. - (u.z[-1,0,-1] + u.z[-1,0,0])/4.) #endif )/sq(Delta); if (fabs (res.x[]) > maxres) maxres = fabs (res.x[]); } #endif return maxres; } #undef lambda trace mgstats viscosity (struct Viscosity p) { vector u = p.u, r[]; foreach() foreach_dimension() r.x[] = u.x[]; face vector mu = p.mu; scalar rho = p.rho; restriction ({mu,rho}); return mg_solve ((scalar *){u}, (scalar *){r}, residual_viscosity, relax_viscosity, &p, p.nrelax, p.res); } trace mgstats viscosity_explicit (struct Viscosity p) { vector u = p.u, r[]; mgstats mg = {0}; mg.resb = residual_viscosity ((scalar *){u}, (scalar *){u}, (scalar *){r}, &p); foreach() foreach_dimension() u.x[] += r.x[]; boundary ((scalar *){u}); return mg; }