Added a proof-of-concept helical forcing which uses the newly introduced ScalarArrays for reading profiles. Not extensively tested.

This commit is contained in:
jpekkila
2019-09-02 21:29:07 +03:00
parent 9e57aba9b7
commit cdb504e772
4 changed files with 597 additions and 0 deletions

5
acc/pc_mhd_solver/.gitignore vendored Normal file
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build
testbin
# Except this file
!.gitignore

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#include "stencil_definition.sdh"
Preprocessed Scalar
value(in ScalarField vertex)
{
return vertex[vertexIdx];
}
Preprocessed Vector
gradient(in ScalarField vertex)
{
return (Vector){derx(vertexIdx, vertex), dery(vertexIdx, vertex), derz(vertexIdx, vertex)};
}
#if LUPWD
Preprocessed Scalar
der6x_upwd(in ScalarField vertex)
{
Scalar inv_ds = AC_inv_dsx;
return (Scalar){Scalar(1.0 / 60.0) * inv_ds *
(-Scalar(20.0) * vertex[vertexIdx.x, vertexIdx.y, vertexIdx.z] +
Scalar(15.0) * (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] +
vertex[vertexIdx.x - 2, vertexIdx.y, vertexIdx.z]) +
vertex[vertexIdx.x + 3, vertexIdx.y, vertexIdx.z] +
vertex[vertexIdx.x - 3, vertexIdx.y, vertexIdx.z])};
}
Preprocessed Scalar
der6y_upwd(in ScalarField vertex)
{
Scalar inv_ds = AC_inv_dsy;
return (Scalar){Scalar(1.0 / 60.0) * inv_ds *
(-Scalar(20.0) * vertex[vertexIdx.x, vertexIdx.y, vertexIdx.z] +
Scalar(15.0) * (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] +
vertex[vertexIdx.x, vertexIdx.y - 2, vertexIdx.z]) +
vertex[vertexIdx.x, vertexIdx.y + 3, vertexIdx.z] +
vertex[vertexIdx.x, vertexIdx.y - 3, vertexIdx.z])};
}
Preprocessed Scalar
der6z_upwd(in ScalarField vertex)
{
Scalar inv_ds = AC_inv_dsz;
return (Scalar){Scalar(1.0 / 60.0) * inv_ds *
(-Scalar(20.0) * vertex[vertexIdx.x, vertexIdx.y, vertexIdx.z] +
Scalar(15.0) * (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] +
vertex[vertexIdx.x, vertexIdx.y, vertexIdx.z - 2]) +
vertex[vertexIdx.x, vertexIdx.y, vertexIdx.z + 3] +
vertex[vertexIdx.x, vertexIdx.y, vertexIdx.z - 3])};
}
#endif
Preprocessed Matrix
hessian(in ScalarField vertex)
{
Matrix hessian;
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[2] = (Vector){hessian.row[0].z, hessian.row[1].z, derzz(vertexIdx, vertex)};
return hessian;
}

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#define LDENSITY (1)
#define LHYDRO (1)
#define LMAGNETIC (1)
#define LENTROPY (1)
#define LTEMPERATURE (0)
#define LFORCING (1)
#define LUPWD (1)
#define AC_THERMAL_CONDUCTIVITY (AcReal(0.001)) // TODO: make an actual config parameter
// Int params
uniform int AC_max_steps;
uniform int AC_save_steps;
uniform int AC_bin_steps;
uniform int AC_bc_type;
// Real params
uniform Scalar AC_dt;
// Spacing
uniform Scalar AC_dsx;
uniform Scalar AC_dsy;
uniform Scalar AC_dsz;
uniform Scalar AC_dsmin;
// physical grid
uniform Scalar AC_xlen;
uniform Scalar AC_ylen;
uniform Scalar AC_zlen;
uniform Scalar AC_xorig;
uniform Scalar AC_yorig;
uniform Scalar AC_zorig;
// Physical units
uniform Scalar AC_unit_density;
uniform Scalar AC_unit_velocity;
uniform Scalar AC_unit_length;
// properties of gravitating star
uniform Scalar AC_star_pos_x;
uniform Scalar AC_star_pos_y;
uniform Scalar AC_star_pos_z;
uniform Scalar AC_M_star;
// Run params
uniform Scalar AC_cdt;
uniform Scalar AC_cdtv;
uniform Scalar AC_cdts;
uniform Scalar AC_nu_visc;
uniform Scalar AC_cs_sound;
uniform Scalar AC_eta;
uniform Scalar AC_mu0;
uniform Scalar AC_cp_sound;
uniform Scalar AC_gamma;
uniform Scalar AC_cv_sound;
uniform Scalar AC_lnT0;
uniform Scalar AC_lnrho0;
uniform Scalar AC_zeta;
uniform Scalar AC_trans;
// Other
uniform Scalar AC_bin_save_t;
// Initial condition params
uniform Scalar AC_ampl_lnrho;
uniform Scalar AC_ampl_uu;
uniform Scalar AC_angl_uu;
uniform Scalar AC_lnrho_edge;
uniform Scalar AC_lnrho_out;
// Forcing parameters. User configured.
uniform Scalar AC_forcing_magnitude;
uniform Scalar AC_relhel;
uniform Scalar AC_kmin;
uniform Scalar AC_kmax;
// Forcing parameters. Set by the generator.
uniform Scalar AC_forcing_phase;
uniform Scalar AC_k_forcex;
uniform Scalar AC_k_forcey;
uniform Scalar AC_k_forcez;
uniform Scalar AC_kaver;
uniform Scalar AC_ff_hel_rex;
uniform Scalar AC_ff_hel_rey;
uniform Scalar AC_ff_hel_rez;
uniform Scalar AC_ff_hel_imx;
uniform Scalar AC_ff_hel_imy;
uniform Scalar AC_ff_hel_imz;
// Additional helper params // (deduced from other params do not set these directly!)
uniform Scalar AC_G_CONST;
uniform Scalar AC_GM_star;
uniform Scalar AC_sq2GM_star;
uniform Scalar AC_cs2_sound;
uniform Scalar AC_inv_dsx;
uniform Scalar AC_inv_dsy;
uniform Scalar AC_inv_dsz;
// PC-style helical forcing with profiles
uniform Vector AC_kk;
uniform Vector AC_coef1;
uniform Vector AC_coef2;
uniform Vector AC_coef3;
uniform Vector AC_fda;
uniform Scalar AC_phase;
uniform Scalar AC_fact;
uniform Scalar AC_k1_ff;
uniform ScalarArray AC_profx;
uniform ScalarArray AC_profy;
uniform ScalarArray AC_profz;
uniform ScalarArray AC_profx_hel;
uniform ScalarArray AC_profy_hel;
uniform ScalarArray AC_profz_hel;
uniform int AC_iforcing_zsym;
uniform ScalarArray AC_0;
uniform ScalarArray AC_1;
uniform ScalarArray AC_2;
uniform ScalarArray AC_3;
uniform ScalarArray AC_4;
uniform ScalarArray AC_5;
uniform ScalarArray AC_6;
uniform ScalarArray AC_7;
uniform ScalarArray AC_8;
uniform ScalarArray AC_9;
uniform ScalarArray AC_10;
uniform ScalarArray AC_11;
uniform ScalarArray AC_12;
uniform ScalarArray AC_13;
uniform ScalarArray AC_14;
uniform ScalarArray AC_15;
uniform ScalarArray AC_16;
uniform ScalarArray AC_17;
uniform ScalarArray AC_18;
uniform ScalarArray AC_19;
/*
* =============================================================================
* User-defined vertex buffers
* =============================================================================
*/
#if LENTROPY
uniform ScalarField VTXBUF_LNRHO;
uniform ScalarField VTXBUF_UUX;
uniform ScalarField VTXBUF_UUY;
uniform ScalarField VTXBUF_UUZ;
uniform ScalarField VTXBUF_AX;
uniform ScalarField VTXBUF_AY;
uniform ScalarField VTXBUF_AZ;
uniform ScalarField VTXBUF_ENTROPY;
#elif LMAGNETIC
uniform ScalarField VTXBUF_LNRHO;
uniform ScalarField VTXBUF_UUX;
uniform ScalarField VTXBUF_UUY;
uniform ScalarField VTXBUF_UUZ;
uniform ScalarField VTXBUF_AX;
uniform ScalarField VTXBUF_AY;
uniform ScalarField VTXBUF_AZ;
#elif LHYDRO
uniform ScalarField VTXBUF_LNRHO;
uniform ScalarField VTXBUF_UUX;
uniform ScalarField VTXBUF_UUY;
uniform ScalarField VTXBUF_UUZ;
#else
uniform ScalarField VTXBUF_LNRHO;
#endif

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#include "stencil_definition.sdh"
Vector
value(in VectorField uu)
{
return (Vector){value(uu.x), value(uu.y), value(uu.z)};
}
#if LUPWD
Scalar
upwd_der6(in VectorField uu, in ScalarField lnrho)
{
Scalar uux = fabs(value(uu).x);
Scalar uuy = fabs(value(uu).y);
Scalar uuz = fabs(value(uu).z);
return (Scalar){uux * der6x_upwd(lnrho) + uuy * der6y_upwd(lnrho) + uuz * der6z_upwd(lnrho)};
}
#endif
Matrix
gradients(in VectorField uu)
{
return (Matrix){gradient(uu.x), gradient(uu.y), gradient(uu.z)};
}
Scalar
continuity(in VectorField uu, in ScalarField lnrho)
{
return -dot(value(uu), gradient(lnrho))
#if LUPWD
// This is a corrective hyperdiffusion term for upwinding.
+ upwd_der6(uu, lnrho)
#endif
- divergence(uu);
}
#if LENTROPY
Vector
momentum(in VectorField uu, in ScalarField lnrho, in ScalarField ss, in VectorField aa)
{
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 Vector j = (Scalar(1.) / AC_mu0) *
(gradient_of_divergence(aa) - laplace_vec(aa)); // Current density
const Vector B = curl(aa);
// TODO: DOES INTHERMAL VERSTION INCLUDE THE MAGNETIC FIELD?
const Scalar inv_rho = Scalar(1.) / exp(value(lnrho));
// Regex replace CPU constants with get\(AC_([a-zA-Z_0-9]*)\)
// \1
const Vector mom = -mul(gradients(uu), value(uu)) -
cs2 * ((Scalar(1.) / AC_cp_sound) * gradient(ss) + gradient(lnrho)) +
inv_rho * cross(j, B) +
AC_nu_visc *
(laplace_vec(uu) + Scalar(1. / 3.) * gradient_of_divergence(uu) +
Scalar(2.) * mul(S, gradient(lnrho))) +
AC_zeta * gradient_of_divergence(uu);
return mom;
}
#elif LTEMPERATURE
Vector
momentum(in VectorField uu, in ScalarField lnrho, in ScalarField tt)
{
Vector mom;
const Matrix S = stress_tensor(uu);
const Vector pressure_term = (AC_cp_sound - AC_cv_sound) *
(gradient(tt) + value(tt) * gradient(lnrho));
mom = -mul(gradients(uu), value(uu)) - pressure_term +
AC_nu_visc * (laplace_vec(uu) + Scalar(1. / 3.) * gradient_of_divergence(uu) +
Scalar(2.) * mul(S, gradient(lnrho))) +
AC_zeta * gradient_of_divergence(uu);
#if LGRAVITY
mom = mom - (Vector){0, 0, -10.0};
#endif
return mom;
}
#else
Vector
momentum(in VectorField uu, in ScalarField lnrho)
{
Vector mom;
const Matrix S = stress_tensor(uu);
// Isothermal: we have constant speed of sound
mom = -mul(gradients(uu), value(uu)) - AC_cs2_sound * gradient(lnrho) +
AC_nu_visc * (laplace_vec(uu) + Scalar(1. / 3.) * gradient_of_divergence(uu) +
Scalar(2.) * mul(S, gradient(lnrho))) +
AC_zeta * gradient_of_divergence(uu);
#if LGRAVITY
mom = mom - (Vector){0, 0, -10.0};
#endif
return mom;
}
#endif
Vector
induction(in VectorField uu, in VectorField aa)
{
// 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,
// yes this actually works. See pg.28 in arXiv:astro-ph/0109497)
// u cross B - AC_eta * AC_mu0 * (AC_mu0^-1 * [- laplace A + grad div A ])
const Vector B = curl(aa);
const Vector grad_div = gradient_of_divergence(aa);
const Vector lap = laplace_vec(aa);
// Note, AC_mu0 is cancelled out
const Vector ind = cross(value(uu), B) - AC_eta * (grad_div - lap);
return ind;
}
#if LENTROPY
Scalar
lnT(in ScalarField ss, in ScalarField lnrho)
{
const Scalar lnT = AC_lnT0 + AC_gamma * value(ss) / AC_cp_sound +
(AC_gamma - Scalar(1.)) * (value(lnrho) - AC_lnrho0);
return lnT;
}
// Nabla dot (K nabla T) / (rho T)
Scalar
heat_conduction(in ScalarField ss, in ScalarField lnrho)
{
const Scalar inv_AC_cp_sound = AcReal(1.) / AC_cp_sound;
const Vector grad_ln_chi = -gradient(lnrho);
const Scalar first_term = AC_gamma * inv_AC_cp_sound * laplace(ss) +
(AC_gamma - AcReal(1.)) * laplace(lnrho);
const Vector second_term = AC_gamma * inv_AC_cp_sound * gradient(ss) +
(AC_gamma - AcReal(1.)) * gradient(lnrho);
const Vector third_term = AC_gamma * (inv_AC_cp_sound * gradient(ss) + gradient(lnrho)) +
grad_ln_chi;
const Scalar chi = AC_THERMAL_CONDUCTIVITY / (exp(value(lnrho)) * AC_cp_sound);
return AC_cp_sound * chi * (first_term + dot(second_term, third_term));
}
Scalar
heating(const int i, const int j, const int k)
{
return 1;
}
Scalar
entropy(in ScalarField ss, in VectorField uu, in ScalarField lnrho, in VectorField aa)
{
const Matrix S = stress_tensor(uu);
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 Scalar RHS = H_CONST - C_CONST + AC_eta * (AC_mu0)*dot(j, j) +
Scalar(2.) * exp(value(lnrho)) * AC_nu_visc * contract(S) +
AC_zeta * exp(value(lnrho)) * divergence(uu) * divergence(uu);
return -dot(value(uu), gradient(ss)) + inv_pT * RHS + heat_conduction(ss, lnrho);
}
#endif
#if LTEMPERATURE
Scalar
heat_transfer(in VectorField uu, in ScalarField lnrho, in ScalarField tt)
{
const Matrix S = stress_tensor(uu);
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);
}
#endif
#if LFORCING
Vector
simple_vortex_forcing(Vector a, Vector b, Scalar magnitude)
{
return magnitude * cross(normalized(b - a), (Vector){0, 0, 1}); // Vortex
}
Vector
simple_outward_flow_forcing(Vector a, Vector b, Scalar magnitude)
{
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
// helicity
Vector
helical_forcing(Scalar magnitude, Vector k_force, Vector xx, Vector ff_re, Vector ff_im, Scalar phi)
{
// JP: This looks wrong:
// 1) Should it be AC_dsx * AC_nx instead of AC_dsx * AC_ny?
// 2) Should you also use globalGrid.n instead of the local n?
// MV: You are rigth. Made a quickfix. I did not see the error because multigpu is split
// in z direction not y direction.
// 3) Also final point: can we do this with vectors/quaternions instead?
// Tringonometric functions are much more expensive and inaccurate/
// MV: Good idea. No an immediate priority.
// Fun related article:
// https://randomascii.wordpress.com/2014/10/09/intel-underestimates-error-bounds-by-1-3-quintillion/
xx.x = xx.x * (2.0 * M_PI / (AC_dsx * globalGridN.x));
xx.y = xx.y * (2.0 * M_PI / (AC_dsy * globalGridN.y));
xx.z = xx.z * (2.0 * M_PI / (AC_dsz * globalGridN.z));
Scalar cos_phi = cos(phi);
Scalar sin_phi = sin(phi);
Scalar cos_k_dot_x = cos(dot(k_force, xx));
Scalar sin_k_dot_x = sin(dot(k_force, xx));
// Phase affect only the x-component
// Scalar real_comp = cos_k_dot_x;
// Scalar imag_comp = sin_k_dot_x;
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;
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.z * real_comp_phase - ff_im.z * imag_comp_phase};
return force;
}
Vector
forcing_OLD(int3 globalVertexIdx, Scalar dt)
{
Vector a = Scalar(.5) * (Vector){globalGridN.x * AC_dsx, globalGridN.y * AC_dsy,
globalGridN.z * AC_dsz}; // source (origin)
Vector xx = (Vector){(globalVertexIdx.x - DCONST(AC_nx_min)) * AC_dsx,
(globalVertexIdx.y - DCONST(AC_ny_min)) * AC_dsy,
(globalVertexIdx.z - DCONST(AC_nz_min)) * AC_dsz}; // sink (current index)
const Scalar cs2 = AC_cs2_sound;
const Scalar cs = sqrt(cs2);
// Placeholders until determined properly
Scalar magnitude = AC_forcing_magnitude;
Scalar phase = AC_forcing_phase;
Vector k_force = (Vector){AC_k_forcex, AC_k_forcey, AC_k_forcez};
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};
// Determine that forcing funtion type at this point.
// Vector force = simple_vortex_forcing(a, xx, magnitude);
// Vector force = simple_outward_flow_forcing(a, xx, magnitude);
Vector force = helical_forcing(magnitude, k_force, xx, ff_re, ff_im, phase);
// Scaling N = magnitude*cs*sqrt(k*cs/dt) * dt
const Scalar NN = cs * sqrt(AC_kaver * cs);
// MV: Like in the Pencil Code. I don't understandf the logic here.
force.x = sqrt(dt) * NN * force.x;
force.y = sqrt(dt) * NN * force.y;
force.z = sqrt(dt) * NN * force.z;
if (is_valid(force)) {
return force;
}
else {
return (Vector){0, 0, 0};
}
}
// PC-style helical forcing with support for profiles
Vector
forcing(int3 vertexIdx, int3 globalVertexIdx, Scalar dt, ScalarArray profx, ScalarArray profy,
ScalarArray profz, ScalarArray profx_hel, ScalarArray profy_hel, ScalarArray profz_hel)
{
Vector pos = (Vector){(globalVertexIdx.x - DCONST(AC_nx_min)) * AC_dsx,
(globalVertexIdx.y - DCONST(AC_ny_min)) * AC_dsy,
(globalVertexIdx.z - DCONST(AC_nz_min)) * AC_dsz};
Complex fx = AC_fact * exp(Complex(0, AC_kk.x * AC_k1_ff * pos.z + AC_phase));
Complex fy = exp(Complex(0, AC_kk.y * AC_k1_ff * pos.y));
Complex fz;
if (AC_iforcing_zsym == 0) {
fz = exp(Complex(0., AC_kk.z * AC_k1_ff * pos.z));
}
else if (AC_iforcing_zsym == 1) {
fz = Complex(cos(AC_kk.z * AC_k1_ff * pos.z), 0);
}
else if (AC_iforcing_zsym == -1) {
fz = Complex(sin(AC_kk.z * AC_k1_ff * pos.z), 0);
}
else {
// Failure
}
Complex fxyz = fx * fy * fz;
// TODO recheck indices
Scalar force_ampl = profx[vertexIdx.x - NGHOST] * profy[vertexIdx.y] * profz[vertexIdx.z];
Scalar prof_hel_ampl = profx_hel[vertexIdx.x - NGHOST] * profy_hel[vertexIdx.y] *
profz_hel[vertexIdx.z];
return force_ampl * AC_fda * (Complex(AC_coef1.x, prof_hel_ampl * AC_coef2.x) * fxyz).x;
}
#endif // LFORCING
// Declare input and output arrays using locations specified in the
// array enum in astaroth.h
in ScalarField lnrho(VTXBUF_LNRHO);
out ScalarField out_lnrho(VTXBUF_LNRHO);
in VectorField uu(VTXBUF_UUX, VTXBUF_UUY, VTXBUF_UUZ);
out VectorField out_uu(VTXBUF_UUX, VTXBUF_UUY, VTXBUF_UUZ);
#if LMAGNETIC
in VectorField aa(VTXBUF_AX, VTXBUF_AY, VTXBUF_AZ);
out VectorField out_aa(VTXBUF_AX, VTXBUF_AY, VTXBUF_AZ);
#endif
#if LENTROPY
in ScalarField ss(VTXBUF_ENTROPY);
out ScalarField out_ss(VTXBUF_ENTROPY);
#endif
#if LTEMPERATURE
in ScalarField tt(VTXBUF_TEMPERATURE);
out ScalarField out_tt(VTXBUF_TEMPERATURE);
#endif
Kernel void
solve()
{
Scalar dt = AC_dt;
out_lnrho = rk3(out_lnrho, lnrho, continuity(uu, lnrho), dt);
#if LMAGNETIC
out_aa = rk3(out_aa, aa, induction(uu, aa), dt);
#endif
#if LENTROPY
out_uu = rk3(out_uu, uu, momentum(uu, lnrho, ss, aa), dt);
out_ss = rk3(out_ss, ss, entropy(ss, uu, lnrho, aa), dt);
#elif LTEMPERATURE
out_uu = rk3(out_uu, uu, momentum(uu, lnrho, tt), dt);
out_tt = rk3(out_tt, tt, heat_transfer(uu, lnrho, tt), dt);
#else
out_uu = rk3(out_uu, uu, momentum(uu, lnrho), dt);
#endif
#if LFORCING
if (step_number == 2) {
out_uu = out_uu + forcing(vertexIdx, globalVertexIdx, dt, AC_profx, AC_profy, AC_profz,
AC_profx_hel, AC_profy_hel, AC_profz_hel);
}
#endif
}