void Test_TransportVP_ImposedData(const real *x, const real t, real *w) {
for(int i = 0; i <_INDEX_MAX_KIN + 1; i++) {
int j = i % _DEG_V; // local connectivity put in function
int nel = i / _DEG_V; // element num (TODO : function)
real vi = (-_VMAX + nel * _DV + _DV * glop(_DEG_V, j));
w[i] = TransportVP_ImposedKinetic_Data(x, t, vi);
}
// exact value of the potential and electric field
w[_INDEX_PHI] = -x[0];
w[_INDEX_EX] = 1;
w[_INDEX_RHO] = 0.; //rho init
w[_INDEX_VELOCITY] = 0; // u init
w[_INDEX_PRESSURE] = 0; // p init
w[_INDEX_TEMP] = 0; // e ou T init
}
real local_kinetic_energy(field *f,real *x, real *w) {
real wex[_INDEX_MAX];
real l_ke=0;
real t=f->tnow;
// loop on the finite emlements
for(int iel = 0; iel < _NB_ELEM_V; iel++){
// loop on the local glops
for(int iloc = 0; iloc < _DEG_V + 1; iloc++){
real omega = wglop(_DEG_V, iloc);
real vi = -_VMAX + iel * _DV + _DV * glop(_DEG_V, iloc);
int ipg = iloc + iel * _DEG_V;
l_ke += omega * _DV * w[ipg] * vi * vi ;
}
}
return l_ke;
}
void TestPoisson_ImposedData(const real x[3], const real t,real w[]){
for(int i = 0; i < _INDEX_MAX_KIN + 1; i++){
int j = i%_DEG_V; // local connectivity put in function
int nel = i / _DEG_V; // element num (TODO : function)
real vi = (-_VMAX + nel * _DV + _DV * glop(_DEG_V, j));
w[i] = 1. / _VMAX;
}
// exact value of the potential
// and electric field
w[_INDEX_PHI] = x[0] * (1 - x[0]);
w[_INDEX_EX] = -1. + 2. * x[0];
w[_INDEX_RHO] = 2.; //rho init
w[_INDEX_VELOCITY] = 0; // u init
w[_INDEX_PRESSURE] = 0; // p init
w[_INDEX_TEMP] = 0; // e ou T init
};
//! \brief compute square of velocity L2 error
//! \param[in] w : values of f at glops
//! \param[in] x : point of the mesh
//! \param[in] t : time
//! \param[in] t : type of L2norm. if type_norm=0 this is the
//! numerical solution if type_norm=1 this is the error
real L2VelError(field *f, real *x, real *w){
real wex[_INDEX_MAX];
real err2 = 0;
real t = f->tnow;
f->model.ImposedData(x, t, wex);
// loop on the finite emlements
for(int iel = 0; iel < _NB_ELEM_V; iel++){
// loop on the local glops
for(int iloc = 0; iloc < _DEG_V + 1; iloc++){
real omega = wglop(_DEG_V, iloc);
real vi = -_VMAX + iel*_DV + _DV * glop(_DEG_V, iloc);
int ipg = iloc + iel * _DEG_V;
err2 += omega * _DV * (w[ipg] - wex[ipg]) * (w[ipg] - wex[ipg]);
}
}
return err2;
}
void TestPeriodic_ImposedData(const real x[3], const real t,real w[]){
real pi=4*atan(1.);
for(int i=0;i<_INDEX_MAX_KIN+1;i++){
int j=i%_DEG_V; // local connectivity put in function
int nel=i/_DEG_V; // element num (TODO : function)
real vi = (-_VMAX+nel*_DV +
_DV* glop(_DEG_V,j));
w[i]=cos(2*pi*(x[0]-vi*t));
}
// exact value of the potential
// and electric field
w[_INDEX_PHI]=0;
w[_INDEX_EX]=0;
w[_INDEX_RHO]=2.; //rho init
w[_INDEX_VELOCITY]=0; // u init
w[_INDEX_PRESSURE]=0; // p init
w[_INDEX_TEMP]=0; // e ou T init
};
void VlasovP_Lagrangian_NumFlux(real wL[],real wR[],real* vnorm,real* flux)
{
for(int i=0;i<_INDEX_MAX_KIN+1;i++){
int j=i%_DEG_V; // local connectivity put in function
int nel=i/_DEG_V; // element num (TODO : function)
real vn = (-_VMAX+nel*_DV +
_DV* glop(_DEG_V,j))*vnorm[0];
real vnp = vn>0 ? vn : 0;
real vnm = vn-vnp;
flux[i] = vnp * wL[i] + vnm * wR[i];
}
// do not change the potential !
// and the electric field
flux[_INDEX_PHI]=0; // flux for phi
flux[_INDEX_EX]=0; // flux for E
flux[_INDEX_RHO]=0; // flux for rho
flux[_INDEX_VELOCITY]=0; // flux for u
flux[_INDEX_PRESSURE]=0; // flux for p
flux[_INDEX_TEMP]=0; // flux for e ou T
}
int Test_TransportVP()
{
bool test = true;
field f;
init_empty_field(&f);
int vec=1;
f.model.m=_INDEX_MAX; // num of conservative variables f(vi) for
// each vi, phi, E, rho, u, p, e (ou T)
f.model.NumFlux=VlasovP_Lagrangian_NumFlux;
//f.model.Source = NULL;
f.model.InitData = Test_TransportVP_InitData;
f.model.ImposedData = Test_TransportVP_ImposedData;
f.model.BoundaryFlux = Test_TransportVP_BoundaryFlux;
f.varindex = GenericVarindex;
f.interp.interp_param[0] = f.model.m; // _M
f.interp.interp_param[1] = 2; // x direction degree
f.interp.interp_param[2] = 0; // y direction degree
f.interp.interp_param[3] = 0; // z direction degree
f.interp.interp_param[4] = 16; // x direction refinement
f.interp.interp_param[5] = 1; // y direction refinement
f.interp.interp_param[6] = 1; // z direction refinement
// read the gmsh file
ReadMacroMesh(&(f.macromesh), "../test/testcube.msh");
// try to detect a 2d mesh
Detect1DMacroMesh(&(f.macromesh));
bool is1d = f.macromesh.is1d;
assert(is1d);
// mesh preparation
BuildConnectivity(&(f.macromesh));
//AffineMapMacroMesh(&(f.macromesh));
// prepare the initial fields
f.model.cfl = 0.05;
Initfield(&f);
f.vmax = _VMAX; // maximal wave speed
f.nb_diags = 3;
f.pre_dtfield = UpdateVlasovPoisson;
f.post_dtfield=NULL;
f.update_after_rk = PlotVlasovPoisson;
f.model.Source = VlasovP_Lagrangian_Source;
// prudence...
CheckMacroMesh(&(f.macromesh), f.interp.interp_param + 1);
printf("cfl param =%f\n", f.hmin);
real tmax = 0.03;
real dt = set_dt(&f);
RK2(&f, tmax, dt);
//RK2(&f,0.03,0.05);
// save the results and the error
int iel = 2 * _NB_ELEM_V / 3;
int iloc = _DEG_V;
printf("Trace vi=%f\n", -_VMAX + iel * _DV + _DV * glop(_DEG_V, iloc));
Plotfield(iloc + iel * _DEG_V, false, &f, "sol","dgvisu.msh");
Plotfield(iloc + iel * _DEG_V, true, &f, "error","dgerror.msh");
Plot_Energies(&f, dt);
real dd_Kinetic = L2_Kinetic_error(&f);
printf("erreur kinetic L2=%lf\n", dd_Kinetic);
test= test && (dd_Kinetic < 1e-2);
return test;
}