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Autoformatted the DSL files

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This commit is contained in:
jpekkila
2019-08-20 18:41:26 +03:00
parent 73d393e419
commit 5d2b658fb0
2 changed files with 178 additions and 174 deletions
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55
acc/mhd_solver/stencil_assembly.sas
View File

@@ -9,9 +9,7 @@ value(in ScalarField vertex)
Preprocessed Vector Preprocessed Vector
gradient(in ScalarField vertex) gradient(in ScalarField vertex)
{ {
return (Vector){derx(vertexIdx, vertex), return (Vector){derx(vertexIdx, vertex), dery(vertexIdx, vertex), derz(vertexIdx, vertex)};
dery(vertexIdx, vertex),
derz(vertexIdx, vertex)};
} }
#if LUPWD #if LUPWD
@@ -21,14 +19,14 @@ der6x_upwd(in ScalarField vertex)
{ {
Scalar inv_ds = AC_inv_dsx; Scalar inv_ds = AC_inv_dsx;
return (Scalar){ Scalar(1.0/60.0)*inv_ds* ( return (Scalar){Scalar(1.0 / 60.0) * inv_ds *
- Scalar(20.0)* vertex[vertexIdx.x, vertexIdx.y, vertexIdx.z] (-Scalar(20.0) * vertex[vertexIdx.x, vertexIdx.y, vertexIdx.z] +
+ Scalar(15.0)*(vertex[vertexIdx.x+1, vertexIdx.y, vertexIdx.z] Scalar(15.0) * (vertex[vertexIdx.x + 1, vertexIdx.y, vertexIdx.z] +
+ vertex[vertexIdx.x-1, vertexIdx.y, vertexIdx.z]) vertex[vertexIdx.x - 1, vertexIdx.y, vertexIdx.z]) -
- Scalar( 6.0)*(vertex[vertexIdx.x+2, vertexIdx.y, vertexIdx.z] Scalar(6.0) * (vertex[vertexIdx.x + 2, vertexIdx.y, vertexIdx.z] +
+ vertex[vertexIdx.x-2, vertexIdx.y, vertexIdx.z]) vertex[vertexIdx.x - 2, vertexIdx.y, vertexIdx.z]) +
+ vertex[vertexIdx.x+3, vertexIdx.y, vertexIdx.z] vertex[vertexIdx.x + 3, vertexIdx.y, vertexIdx.z] +
+ vertex[vertexIdx.x-3, vertexIdx.y, vertexIdx.z])}; vertex[vertexIdx.x - 3, vertexIdx.y, vertexIdx.z])};
} }
Preprocessed Scalar Preprocessed Scalar
@@ -36,14 +34,14 @@ der6y_upwd(in ScalarField vertex)
{ {
Scalar inv_ds = AC_inv_dsy; Scalar inv_ds = AC_inv_dsy;
return (Scalar){ Scalar(1.0/60.0)*inv_ds* ( return (Scalar){Scalar(1.0 / 60.0) * inv_ds *
-Scalar( 20.0)* vertex[vertexIdx.x, vertexIdx.y, vertexIdx.z] (-Scalar(20.0) * vertex[vertexIdx.x, vertexIdx.y, vertexIdx.z] +
+Scalar( 15.0)*(vertex[vertexIdx.x, vertexIdx.y+1, vertexIdx.z] Scalar(15.0) * (vertex[vertexIdx.x, vertexIdx.y + 1, vertexIdx.z] +
+ vertex[vertexIdx.x, vertexIdx.y-1, vertexIdx.z]) vertex[vertexIdx.x, vertexIdx.y - 1, vertexIdx.z]) -
-Scalar( 6.0)*(vertex[vertexIdx.x, vertexIdx.y+2, vertexIdx.z] Scalar(6.0) * (vertex[vertexIdx.x, vertexIdx.y + 2, vertexIdx.z] +
+ vertex[vertexIdx.x, vertexIdx.y-2, vertexIdx.z]) vertex[vertexIdx.x, vertexIdx.y - 2, vertexIdx.z]) +
+ vertex[vertexIdx.x, vertexIdx.y+3, vertexIdx.z] vertex[vertexIdx.x, vertexIdx.y + 3, vertexIdx.z] +
+ vertex[vertexIdx.x, vertexIdx.y-3, vertexIdx.z])}; vertex[vertexIdx.x, vertexIdx.y - 3, vertexIdx.z])};
} }
Preprocessed Scalar Preprocessed Scalar
@@ -51,14 +49,14 @@ der6z_upwd(in ScalarField vertex)
{ {
Scalar inv_ds = AC_inv_dsz; Scalar inv_ds = AC_inv_dsz;
return (Scalar){ Scalar(1.0/60.0)*inv_ds* ( return (Scalar){Scalar(1.0 / 60.0) * inv_ds *
-Scalar( 20.0)* vertex[vertexIdx.x, vertexIdx.y, vertexIdx.z] (-Scalar(20.0) * vertex[vertexIdx.x, vertexIdx.y, vertexIdx.z] +
+Scalar( 15.0)*(vertex[vertexIdx.x, vertexIdx.y, vertexIdx.z+1] Scalar(15.0) * (vertex[vertexIdx.x, vertexIdx.y, vertexIdx.z + 1] +
+ vertex[vertexIdx.x, vertexIdx.y, vertexIdx.z-1]) vertex[vertexIdx.x, vertexIdx.y, vertexIdx.z - 1]) -
-Scalar( 6.0)*(vertex[vertexIdx.x, vertexIdx.y, vertexIdx.z+2] Scalar(6.0) * (vertex[vertexIdx.x, vertexIdx.y, vertexIdx.z + 2] +
+ vertex[vertexIdx.x, vertexIdx.y, vertexIdx.z-2]) vertex[vertexIdx.x, vertexIdx.y, vertexIdx.z - 2]) +
+ vertex[vertexIdx.x, vertexIdx.y, vertexIdx.z+3] vertex[vertexIdx.x, vertexIdx.y, vertexIdx.z + 3] +
+ vertex[vertexIdx.x, vertexIdx.y, vertexIdx.z-3])}; vertex[vertexIdx.x, vertexIdx.y, vertexIdx.z - 3])};
} }
#endif #endif
@@ -68,7 +66,8 @@ hessian(in ScalarField vertex)
{ {
Matrix hessian; Matrix hessian;
hessian.row[0] = (Vector){derxx(vertexIdx, vertex), derxy(vertexIdx, vertex), derxz(vertexIdx, vertex)}; hessian.row[0] = (Vector){derxx(vertexIdx, vertex), derxy(vertexIdx, vertex),
derxz(vertexIdx, vertex)};
hessian.row[1] = (Vector){hessian.row[0].y, deryy(vertexIdx, vertex), deryz(vertexIdx, vertex)}; hessian.row[1] = (Vector){hessian.row[0].y, deryy(vertexIdx, vertex), deryz(vertexIdx, vertex)};
hessian.row[2] = (Vector){hessian.row[0].z, hessian.row[1].z, derzz(vertexIdx, vertex)}; hessian.row[2] = (Vector){hessian.row[0].z, hessian.row[1].z, derzz(vertexIdx, vertex)};

119
acc/mhd_solver/stencil_process.sps
View File

@@ -1,6 +1,5 @@
#include "stencil_definition.sdh" #include "stencil_definition.sdh"
Vector Vector
value(in VectorField uu) value(in VectorField uu)
{ {
@@ -25,7 +24,8 @@ gradients(in VectorField uu)
} }
Scalar Scalar
continuity(in VectorField uu, in ScalarField lnrho) { continuity(in VectorField uu, in ScalarField lnrho)
{
return -dot(value(uu), gradient(lnrho)) return -dot(value(uu), gradient(lnrho))
#if LUPWD #if LUPWD
// This is a corrective hyperdiffusion term for upwinding. // This is a corrective hyperdiffusion term for upwinding.
@@ -36,41 +36,43 @@ continuity(in VectorField uu, in ScalarField lnrho) {
#if LENTROPY #if LENTROPY
Vector Vector
momentum(in VectorField uu, in ScalarField lnrho, in ScalarField ss, in VectorField aa) { momentum(in VectorField uu, in ScalarField lnrho, in ScalarField ss, in VectorField aa)
{
const Matrix S = stress_tensor(uu); const Matrix S = stress_tensor(uu);
const Scalar cs2 = AC_cs2_sound * exp(AC_gamma * value(ss) / AC_cp_sound + (AC_gamma - 1) * (value(lnrho) - AC_lnrho0)); const Scalar cs2 = AC_cs2_sound * exp(AC_gamma * value(ss) / AC_cp_sound +
const Vector j = (Scalar(1.) / AC_mu0) * (gradient_of_divergence(aa) - laplace_vec(aa)); // Current density (AC_gamma - 1) * (value(lnrho) - AC_lnrho0));
const Vector j = (Scalar(1.) / AC_mu0) *
(gradient_of_divergence(aa) - laplace_vec(aa)); // Current density
const Vector B = curl(aa); const Vector B = curl(aa);
// TODO: DOES INTHERMAL VERSTION INCLUDE THE MAGNETIC FIELD? // TODO: DOES INTHERMAL VERSTION INCLUDE THE MAGNETIC FIELD?
const Scalar inv_rho = Scalar(1.) / exp(value(lnrho)); const Scalar inv_rho = Scalar(1.) / exp(value(lnrho));
// Regex replace CPU constants with get\(AC_([a-zA-Z_0-9]*)\) // Regex replace CPU constants with get\(AC_([a-zA-Z_0-9]*)\)
// \1 // \1
const Vector mom = - mul(gradients(uu), value(uu)) const Vector mom = -mul(gradients(uu), value(uu)) -
- cs2 * ((Scalar(1.) / AC_cp_sound) * gradient(ss) + gradient(lnrho)) cs2 * ((Scalar(1.) / AC_cp_sound) * gradient(ss) + gradient(lnrho)) +
+ inv_rho * cross(j, B) inv_rho * cross(j, B) +
+ AC_nu_visc * ( AC_nu_visc *
laplace_vec(uu) (laplace_vec(uu) + Scalar(1. / 3.) * gradient_of_divergence(uu) +
+ Scalar(1. / 3.) * gradient_of_divergence(uu) Scalar(2.) * mul(S, gradient(lnrho))) +
+ Scalar(2.) * mul(S, gradient(lnrho)) AC_zeta * gradient_of_divergence(uu);
)
+ AC_zeta * gradient_of_divergence(uu);
return mom; return mom;
} }
#elif LTEMPERATURE #elif LTEMPERATURE
Vector Vector
momentum(in VectorField uu, in ScalarField lnrho, in ScalarField tt) { momentum(in VectorField uu, in ScalarField lnrho, in ScalarField tt)
{
Vector mom; Vector mom;
const Matrix S = stress_tensor(uu); const Matrix S = stress_tensor(uu);
const Vector pressure_term = (AC_cp_sound - AC_cv_sound) * (gradient(tt) + value(tt) * gradient(lnrho)); const Vector pressure_term = (AC_cp_sound - AC_cv_sound) *
(gradient(tt) + value(tt) * gradient(lnrho));
mom = -mul(gradients(uu), value(uu)) - mom = -mul(gradients(uu), value(uu)) - pressure_term +
pressure_term + AC_nu_visc * (laplace_vec(uu) + Scalar(1. / 3.) * gradient_of_divergence(uu) +
AC_nu_visc * Scalar(2.) * mul(S, gradient(lnrho))) +
(laplace_vec(uu) + Scalar(1. / 3.) * gradient_of_divergence(uu) + AC_zeta * gradient_of_divergence(uu);
Scalar(2.) * mul(S, gradient(lnrho))) + AC_zeta * gradient_of_divergence(uu);
#if LGRAVITY #if LGRAVITY
mom = mom - (Vector){0, 0, -10.0}; mom = mom - (Vector){0, 0, -10.0};
@@ -80,18 +82,18 @@ momentum(in VectorField uu, in ScalarField lnrho, in ScalarField tt) {
} }
#else #else
Vector Vector
momentum(in VectorField uu, in ScalarField lnrho) { momentum(in VectorField uu, in ScalarField lnrho)
{
Vector mom; Vector mom;
const Matrix S = stress_tensor(uu); const Matrix S = stress_tensor(uu);
// Isothermal: we have constant speed of sound // Isothermal: we have constant speed of sound
mom = -mul(gradients(uu), value(uu)) - mom = -mul(gradients(uu), value(uu)) - AC_cs2_sound * gradient(lnrho) +
AC_cs2_sound * gradient(lnrho) + AC_nu_visc * (laplace_vec(uu) + Scalar(1. / 3.) * gradient_of_divergence(uu) +
AC_nu_visc * Scalar(2.) * mul(S, gradient(lnrho))) +
(laplace_vec(uu) + Scalar(1. / 3.) * gradient_of_divergence(uu) + AC_zeta * gradient_of_divergence(uu);
Scalar(2.) * mul(S, gradient(lnrho))) + AC_zeta * gradient_of_divergence(uu);
#if LGRAVITY #if LGRAVITY
mom = mom - (Vector){0, 0, -10.0}; mom = mom - (Vector){0, 0, -10.0};
@@ -101,9 +103,9 @@ momentum(in VectorField uu, in ScalarField lnrho) {
} }
#endif #endif
Vector Vector
induction(in VectorField uu, in VectorField aa) { induction(in VectorField uu, in VectorField aa)
{
// Note: We do (-nabla^2 A + nabla(nabla dot A)) instead of (nabla x (nabla // Note: We do (-nabla^2 A + nabla(nabla dot A)) instead of (nabla x (nabla
// x A)) in order to avoid taking the first derivative twice (did the math, // x A)) in order to avoid taking the first derivative twice (did the math,
// yes this actually works. See pg.28 in arXiv:astro-ph/0109497) // yes this actually works. See pg.28 in arXiv:astro-ph/0109497)
@@ -118,10 +120,10 @@ induction(in VectorField uu, in VectorField aa) {
return ind; return ind;
} }
#if LENTROPY #if LENTROPY
Scalar Scalar
lnT( in ScalarField ss, in ScalarField lnrho) { lnT(in ScalarField ss, in ScalarField lnrho)
{
const Scalar lnT = AC_lnT0 + AC_gamma * value(ss) / AC_cp_sound + const Scalar lnT = AC_lnT0 + AC_gamma * value(ss) / AC_cp_sound +
(AC_gamma - Scalar(1.)) * (value(lnrho) - AC_lnrho0); (AC_gamma - Scalar(1.)) * (value(lnrho) - AC_lnrho0);
return lnT; return lnT;
@@ -129,7 +131,8 @@ lnT( in ScalarField ss, in ScalarField lnrho) {
// Nabla dot (K nabla T) / (rho T) // Nabla dot (K nabla T) / (rho T)
Scalar Scalar
heat_conduction( in ScalarField ss, in ScalarField lnrho) { heat_conduction(in ScalarField ss, in ScalarField lnrho)
{
const Scalar inv_AC_cp_sound = AcReal(1.) / AC_cp_sound; const Scalar inv_AC_cp_sound = AcReal(1.) / AC_cp_sound;
const Vector grad_ln_chi = -gradient(lnrho); const Vector grad_ln_chi = -gradient(lnrho);
@@ -138,31 +141,31 @@ heat_conduction( in ScalarField ss, in ScalarField lnrho) {
(AC_gamma - AcReal(1.)) * laplace(lnrho); (AC_gamma - AcReal(1.)) * laplace(lnrho);
const Vector second_term = AC_gamma * inv_AC_cp_sound * gradient(ss) + const Vector second_term = AC_gamma * inv_AC_cp_sound * gradient(ss) +
(AC_gamma - AcReal(1.)) * gradient(lnrho); (AC_gamma - AcReal(1.)) * gradient(lnrho);
const Vector third_term = AC_gamma * (inv_AC_cp_sound * gradient(ss) + const Vector third_term = AC_gamma * (inv_AC_cp_sound * gradient(ss) + gradient(lnrho)) +
gradient(lnrho)) + grad_ln_chi; grad_ln_chi;
const Scalar chi = AC_THERMAL_CONDUCTIVITY / (exp(value(lnrho)) * AC_cp_sound); const Scalar chi = AC_THERMAL_CONDUCTIVITY / (exp(value(lnrho)) * AC_cp_sound);
return AC_cp_sound * chi * (first_term + dot(second_term, third_term)); return AC_cp_sound * chi * (first_term + dot(second_term, third_term));
} }
Scalar Scalar
heating(const int i, const int j, const int k) { heating(const int i, const int j, const int k)
{
return 1; return 1;
} }
Scalar Scalar
entropy(in ScalarField ss, in VectorField uu, in ScalarField lnrho, in VectorField aa) { entropy(in ScalarField ss, in VectorField uu, in ScalarField lnrho, in VectorField aa)
{
const Matrix S = stress_tensor(uu); const Matrix S = stress_tensor(uu);
const Scalar inv_pT = Scalar(1.) / (exp(value(lnrho)) * exp(lnT(ss, lnrho))); const Scalar inv_pT = Scalar(1.) / (exp(value(lnrho)) * exp(lnT(ss, lnrho)));
const Vector j = (Scalar(1.) / AC_mu0) * (gradient_of_divergence(aa) - laplace_vec(aa)); // Current density const Vector j = (Scalar(1.) / AC_mu0) *
const Scalar RHS = H_CONST - C_CONST (gradient_of_divergence(aa) - laplace_vec(aa)); // Current density
+ AC_eta * (AC_mu0) * dot(j, j) const Scalar RHS = H_CONST - C_CONST + AC_eta * (AC_mu0)*dot(j, j) +
+ Scalar(2.) * exp(value(lnrho)) * AC_nu_visc * contract(S) Scalar(2.) * exp(value(lnrho)) * AC_nu_visc * contract(S) +
+ AC_zeta * exp(value(lnrho)) * divergence(uu) * divergence(uu); AC_zeta * exp(value(lnrho)) * divergence(uu) * divergence(uu);
return - dot(value(uu), gradient(ss)) return -dot(value(uu), gradient(ss)) + inv_pT * RHS + heat_conduction(ss, lnrho);
+ inv_pT * RHS
+ heat_conduction(ss, lnrho);
} }
#endif #endif
@@ -172,12 +175,13 @@ heat_transfer(in VectorField uu, in ScalarField lnrho, in ScalarField tt)
{ {
const Matrix S = stress_tensor(uu); const Matrix S = stress_tensor(uu);
const Scalar heat_diffusivity_k = 0.0008; // 8e-4; const Scalar heat_diffusivity_k = 0.0008; // 8e-4;
return -dot(value(uu), gradient(tt)) + heat_diffusivity_k * laplace(tt) + heat_diffusivity_k * dot(gradient(lnrho), gradient(tt)) + AC_nu_visc * contract(S) * (Scalar(1.) / AC_cv_sound) - (AC_gamma - 1) * value(tt) * divergence(uu); return -dot(value(uu), gradient(tt)) + heat_diffusivity_k * laplace(tt) +
heat_diffusivity_k * dot(gradient(lnrho), gradient(tt)) +
AC_nu_visc * contract(S) * (Scalar(1.) / AC_cv_sound) -
(AC_gamma - 1) * value(tt) * divergence(uu);
} }
#endif #endif
#if LFORCING #if LFORCING
Vector Vector
simple_vortex_forcing(Vector a, Vector b, Scalar magnitude) simple_vortex_forcing(Vector a, Vector b, Scalar magnitude)
@@ -191,8 +195,8 @@ simple_outward_flow_forcing(Vector a, Vector b, Scalar magnitude)
return magnitude * (1 / length(b - a)) * normalized(b - a); // Outward flow return magnitude * (1 / length(b - a)) * normalized(b - a); // Outward flow
} }
// The Pencil Code forcing_hel_noshear(), manual Eq. 222, inspired forcing function with adjustable
// The Pencil Code forcing_hel_noshear(), manual Eq. 222, inspired forcing function with adjustable helicity // helicity
Vector Vector
helical_forcing(Scalar magnitude, Vector k_force, Vector xx, Vector ff_re, Vector ff_im, Scalar phi) helical_forcing(Scalar magnitude, Vector k_force, Vector xx, Vector ff_re, Vector ff_im, Scalar phi)
{ {
@@ -220,7 +224,6 @@ helical_forcing(Scalar magnitude, Vector k_force, Vector xx, Vector ff_re, Vecto
Scalar real_comp_phase = cos_k_dot_x * cos_phi - sin_k_dot_x * sin_phi; Scalar real_comp_phase = cos_k_dot_x * cos_phi - sin_k_dot_x * sin_phi;
Scalar imag_comp_phase = cos_k_dot_x * sin_phi + sin_k_dot_x * cos_phi; Scalar imag_comp_phase = cos_k_dot_x * sin_phi + sin_k_dot_x * cos_phi;
Vector force = (Vector){ff_re.x * real_comp_phase - ff_im.x * imag_comp_phase, Vector force = (Vector){ff_re.x * real_comp_phase - ff_im.x * imag_comp_phase,
ff_re.y * real_comp_phase - ff_im.y * imag_comp_phase, ff_re.y * real_comp_phase - ff_im.y * imag_comp_phase,
ff_re.z * real_comp_phase - ff_im.z * imag_comp_phase}; ff_re.z * real_comp_phase - ff_im.z * imag_comp_phase};
@@ -231,8 +234,7 @@ helical_forcing(Scalar magnitude, Vector k_force, Vector xx, Vector ff_re, Vecto
Vector Vector
forcing(int3 globalVertexIdx, Scalar dt) forcing(int3 globalVertexIdx, Scalar dt)
{ {
Vector a = Scalar(.5) * (Vector){globalGridN.x * AC_dsx, Vector a = Scalar(.5) * (Vector){globalGridN.x * AC_dsx, globalGridN.y * AC_dsy,
globalGridN.y * AC_dsy,
globalGridN.z * AC_dsz}; // source (origin) globalGridN.z * AC_dsz}; // source (origin)
Vector xx = (Vector){(globalVertexIdx.x - DCONST(AC_nx_min)) * AC_dsx, Vector xx = (Vector){(globalVertexIdx.x - DCONST(AC_nx_min)) * AC_dsx,
(globalVertexIdx.y - DCONST(AC_ny_min)) * AC_dsy, (globalVertexIdx.y - DCONST(AC_ny_min)) * AC_dsy,
@@ -247,7 +249,6 @@ forcing(int3 globalVertexIdx, Scalar dt)
Vector ff_re = (Vector){AC_ff_hel_rex, AC_ff_hel_rey, AC_ff_hel_rez}; Vector ff_re = (Vector){AC_ff_hel_rex, AC_ff_hel_rey, AC_ff_hel_rez};
Vector ff_im = (Vector){AC_ff_hel_imx, AC_ff_hel_imy, AC_ff_hel_imz}; Vector ff_im = (Vector){AC_ff_hel_imx, AC_ff_hel_imy, AC_ff_hel_imz};
// Determine that forcing funtion type at this point. // Determine that forcing funtion type at this point.
// Vector force = simple_vortex_forcing(a, xx, magnitude); // Vector force = simple_vortex_forcing(a, xx, magnitude);
// Vector force = simple_outward_flow_forcing(a, xx, magnitude); // Vector force = simple_outward_flow_forcing(a, xx, magnitude);
@@ -260,8 +261,12 @@ forcing(int3 globalVertexIdx, Scalar dt)
force.y = sqrt(dt) * NN * force.y; force.y = sqrt(dt) * NN * force.y;
force.z = sqrt(dt) * NN * force.z; force.z = sqrt(dt) * NN * force.z;
if (is_valid(force)) { return force; } if (is_valid(force)) {
else { return (Vector){0, 0, 0}; } return force;
}
else {
return (Vector){0, 0, 0};
}
} }
#endif // LFORCING #endif // LFORCING
@@ -273,7 +278,6 @@ out ScalarField out_lnrho(VTXBUF_LNRHO);
in VectorField uu(VTXBUF_UUX, VTXBUF_UUY, VTXBUF_UUZ); in VectorField uu(VTXBUF_UUX, VTXBUF_UUY, VTXBUF_UUZ);
out VectorField out_uu(VTXBUF_UUX, VTXBUF_UUY, VTXBUF_UUZ); out VectorField out_uu(VTXBUF_UUX, VTXBUF_UUY, VTXBUF_UUZ);
#if LMAGNETIC #if LMAGNETIC
in VectorField aa(VTXBUF_AX, VTXBUF_AY, VTXBUF_AZ); in VectorField aa(VTXBUF_AX, VTXBUF_AY, VTXBUF_AZ);
out VectorField out_aa(VTXBUF_AX, VTXBUF_AY, VTXBUF_AZ); out VectorField out_aa(VTXBUF_AX, VTXBUF_AY, VTXBUF_AZ);
@@ -290,7 +294,8 @@ out ScalarField out_tt(VTXBUF_TEMPERATURE);
#endif #endif
Kernel void Kernel void
solve(Scalar dt) { solve(Scalar dt)
{
out_lnrho = rk3(out_lnrho, lnrho, continuity(uu, lnrho), dt); out_lnrho = rk3(out_lnrho, lnrho, continuity(uu, lnrho), dt);
#if LMAGNETIC #if LMAGNETIC