// This is a user-supplied routine that sets the the boundary conditions
//
void SetBndValues_Unst(const mesh& Mesh, dTensor3* q, dTensor3* aux)
{
int meqn = q->getsize(2);
int kmax = q->getsize(3);
int maux = aux->getsize(2);
int NumElems = Mesh.get_NumElems();
int NumPhysElems = Mesh.get_NumPhysElems();
int NumGhostElems = Mesh.get_NumGhostElems();
int NumNodes = Mesh.get_NumNodes();
int NumPhysNodes = Mesh.get_NumPhysNodes();
int NumEdges = Mesh.get_NumEdges();
// ----------------------------------------
// Loop over each ghost cell element and
// place the correct information into
// these elements
// ----------------------------------------
for (int i=1; i<=NumGhostElems; i++)
{
int j = Mesh.get_ghost_link(i);
for (int m=1; m<=meqn; m++)
for (int k=1; k<=kmax; k++)
{
q->set(i+NumPhysElems,m,k, 0.0 );
}
}
}
// This is a user-supplied routine that sets the the boundary conditions
//
// The default routine for the 4D Vlasov code is to apply zero boundary
// conditions in configuration space. This routine is identical to the one
// found in the unst branch of the 2D DoGPack code, and *should* be setting
// periodic boundary conditions.
//
void SetBndValues_Unst(const mesh& Mesh, dTensor3* q, dTensor3* aux)
{
// problem information (If this were to be pulled from DogParams, these
// numbers would NOT be correct! The reason is that each quadrature point
// was actually saved as a separate "equation")
const int meqn = q->getsize(2);
const int kmax = q->getsize(3);
const int maux = aux->getsize(2);
// Mesh information
const int NumElems = Mesh.get_NumElems();
const int NumPhysElems = Mesh.get_NumPhysElems();
const int NumGhostElems = Mesh.get_NumGhostElems();
const int NumNodes = Mesh.get_NumNodes();
const int NumPhysNodes = Mesh.get_NumPhysNodes();
const int NumEdges = Mesh.get_NumEdges();
// ----------------------------------------
// Loop over each ghost cell element and
// place the correct information into
// these elements
// ----------------------------------------
for (int i=1; i<=NumGhostElems; i++)
{
int j = Mesh.get_ghost_link(i);
for (int m=1; m<=meqn; m++)
for (int k=1; k<=kmax; k++)
{
q->set(i+NumPhysElems, m, k, q->get(j, m, k) );
}
}
}
//
// Output basic mesh information to screen
//
void ScreenOutput(const mesh& Mesh)
{
// Compute mesh quality parameters
double totalarea = Mesh.get_area_prim(1);
double maxarea = Mesh.get_area_prim(1);
double minarea = Mesh.get_area_prim(1);
for (int i=2; i<=Mesh.get_NumPhysElems(); i++)
{
double tmp = Mesh.get_area_prim(i);
totalarea = totalarea + tmp;
if (tmp < minarea)
{ minarea = tmp; }
if (tmp > maxarea)
{ maxarea = tmp; }
}
double minAngle = 180.0;
for (int i=1; i<=Mesh.get_NumPhysElems(); i++)
{
const int i1 = Mesh.get_tnode(i,1);
const int i2 = Mesh.get_tnode(i,2);
const int i3 = Mesh.get_tnode(i,3);
point v12, v23, v31;
v12.x = Mesh.get_node(i2,1) - Mesh.get_node(i1,1);
v12.y = Mesh.get_node(i2,2) - Mesh.get_node(i1,2);
v23.x = Mesh.get_node(i3,1) - Mesh.get_node(i2,1);
v23.y = Mesh.get_node(i3,2) - Mesh.get_node(i2,2);
v31.x = Mesh.get_node(i1,1) - Mesh.get_node(i3,1);
v31.y = Mesh.get_node(i1,2) - Mesh.get_node(i3,2);
double angle1 = acos((v12.x*-v31.x+v12.y*-v31.y)
/(sqrt(v12.x*v12.x+v12.y*v12.y)*sqrt(v31.x*v31.x+v31.y*v31.y)));
double angle2 = acos((v23.x*-v12.x+v23.y*-v12.y)
/(sqrt(v23.x*v23.x+v23.y*v23.y)*sqrt(v12.x*v12.x+v12.y*v12.y)));
double angle3 = acos((v31.x*-v23.x+v31.y*-v23.y)
/(sqrt(v31.x*v31.x+v31.y*v31.y)*sqrt(v23.x*v23.x+v23.y*v23.y)));
if ((angle1*180/pi) < minAngle)
{ minAngle = angle1*180/pi; }
if ((angle2*180/pi) < minAngle)
{ minAngle = angle2*180/pi; }
if ((angle3*180/pi) < minAngle)
{ minAngle = angle3*180/pi; }
}
// Output summary of results to screen
printf("\n");
printf(" SUMMARY OF RESULTS:\n");
printf(" -------------------\n");
printf(" Number of Elements: %8i\n",Mesh.get_NumElems());
printf(" Number of Physical Elements: %8i\n",Mesh.get_NumPhysElems());
printf(" Number of Ghost Elements: %8i\n",Mesh.get_NumGhostElems());
printf(" Number of Nodes: %8i\n",Mesh.get_NumNodes());
printf(" Number of Physical Nodes: %8i\n",Mesh.get_NumPhysNodes());
printf(" Number of Boundary Nodes: %8i\n",Mesh.get_NumBndNodes());
printf(" Number of Edges: %8i\n",Mesh.get_NumEdges());
printf(" Number of Boundary Edges: %8i\n",Mesh.get_NumBndEdges());
printf("\n");
printf(" Total Area Covered: %24.16e\n",totalarea);
printf(" Area Ratio: small/large: %24.16e\n",minarea/maxarea);
printf(" Angle Ratio: minAngle/60: %24.16e\n",minAngle/60.0);
printf("\n");
}
// This file should be identical to DogSolveRK_Unst, with the exception that all
// output printing statements are silenced.
//
// Advance the solution qold to qnew over time interval tstart to tend.
//
// All local information is allocated within this function. The only part
// that gets shared are time values passed through dogStateUnst2. This class
// should be modified to accept the state variable, q and aux in place of only
// containing time information as is currently the case. (-DS)
double DogSolveRK_Unst_Quiet(
const dTensor2* vel_vec,
const mesh& Mesh, const edge_data_Unst& EdgeData,
dTensor3& aux, dTensor3& qold, dTensor3& qnew,
const double tstart, const double tend, DogStateUnst2& dogStateUnst2)
{
const int mx = qnew.getsize(1);
const int meqn = qnew.getsize(2);
const int kmax = qnew.getsize(3);
const int maux = aux.getsize(2);
const double* cflv = dogParams.get_cflv();
const int nv = dogParams.get_nv();
RKinfo rk;
SetRKinfo(dogParams.get_time_order(),rk);
// define local variables
int n_step = 0;
double t = tstart;
double dt = dogStateUnst2.get_initial_dt();
const double CFL_max = cflv[1];
const double CFL_target = cflv[2];
double cfl = 0.0;
double dtmin = dt;
double dtmax = dt;
const int NumElems = Mesh.get_NumElems(); // Number of total elements in mesh
const int NumNodes = Mesh.get_NumNodes(); // Number of nodes in mesh
const int NumEdges = Mesh.get_NumEdges(); // Number of edges in mesh
dTensor3 qstar(NumElems,meqn,kmax);
dTensor3 q1(NumElems,meqn,kmax);
dTensor3 q2(NumElems,meqn,kmax);
dTensor3 auxstar(NumElems,maux,kmax);
dTensor3 Lstar(NumElems,meqn,kmax);
dTensor3 Lold(NumElems,meqn,kmax);
dTensor3 auxold(NumElems,maux,kmax);
dTensor1 smax(NumEdges);
void L2Project_Unst(
const dTensor2* vel_vec,
const int istart, const int iend,
const int QuadOrder, const int BasisOrder_qin, const int BasisOrder_auxin, const
int BasisOrder_fout, const mesh& Mesh, const dTensor3* qin, const dTensor3*
auxin, dTensor3* fout, void (*Func)(const dTensor2* vel_vec, const
dTensor2&,const dTensor2&, const dTensor2&,dTensor2&));
// JUNK here:
void AuxFuncWrapper(
const dTensor2* vel_vec,
const dTensor2& xpts,
const dTensor2& NOT_USED_1,
const dTensor2& NOT_USED_2,
dTensor2& auxvals);
const int space_order = dogParams.get_space_order();
if( maux > 0 )
{
printf("WARNING: maux = %d should be zero for Vlasov routines.", maux);
printf(" Modify parameters.ini to remove this warning\n" );
L2Project_Unst(vel_vec,1,NumElems,
space_order,space_order,space_order,space_order,
Mesh,&qnew,&aux,&aux,&AuxFuncWrapper);
}
// Set initialize qstar and auxstar values
qstar.copyfrom(qold);
auxstar.copyfrom(aux);
// Runge-Kutta time stepping
while (t<tend)
{
// initialize time step
int m_accept = 0;
n_step = n_step + 1;
// check if max number of time steps exceeded
if( n_step > nv )
{
eprintf(" Error in DogSolveRK_Unst.cpp: "
" Exceeded allowed # of time steps \n"
" n_step = %d\n"
" nv = %d\n\n",
n_step, nv);
}
// copy qnew into qold
qold.copyfrom(qnew);
auxold.copyfrom(aux);
// keep trying until we get a dt that does not violate CFL condition
while (m_accept==0)
{
// set current time
double told = t;
if (told+dt > tend)
{ dt = tend - told; }
t = told + dt;
// TODO - this needs to be performed at the 'local' level
dogStateUnst2.set_time ( told );
dogStateUnst2.set_dt ( dt );
// Set initial maximum wave speed to zero
smax.setall(0.);
// Take a full time step of size dt
switch ( dogParams.get_time_order() )
{
case 1: // First order in time (1-stage)
// -----------------------------------------------
// Stage #1 (the only one in this case)
rk.mstage = 1;
BeforeStep_Unst(dt,Mesh,aux,qnew);
ConstructL_Unst(told, vel_vec,Mesh,EdgeData,aux,qnew,Lstar,smax);
UpdateSoln_Unst(rk.alpha1->get(rk.mstage),rk.alpha2->get(rk.mstage),
rk.beta->get(rk.mstage),dt,Mesh,aux, qnew, Lstar, qnew);
AfterStep_Unst(dt,Mesh,aux,qnew);
// -----------------------------------------------
break;
case 2: // Second order in time (2-stages)
// -----------------------------------------------
// Stage #1
rk.mstage = 1;
dogStateUnst2.set_time(told);
BeforeStep_Unst(dt,Mesh,aux,qnew);
ConstructL_Unst(told,vel_vec,Mesh,EdgeData,aux,qnew,Lstar,smax);
UpdateSoln_Unst(
rk.alpha1->get(rk.mstage),rk.alpha2->get(rk.mstage),
rk.beta->get(rk.mstage), dt, Mesh, aux, qnew, Lstar, qstar);
AfterStep_Unst(dt, Mesh, auxstar, qstar);
// ------------------------------------------------
// Stage #2
rk.mstage = 2;
dogStateUnst2.set_time(told+dt);
BeforeStep_Unst(dt, Mesh, auxstar, qstar);
ConstructL_Unst(told+1.0*dt, vel_vec, Mesh, EdgeData, aux, qstar, Lstar, smax);
UpdateSoln_Unst(rk.alpha1->get(rk.mstage), rk.alpha2->get(rk.mstage),
rk.beta->get(rk.mstage), dt, Mesh, auxstar, qstar, Lstar, qnew);
AfterStep_Unst(dt, Mesh, aux, qnew);
// ------------------------------------------------
break;
case 3: // Third order in time (3-stages)
// qnew = alpha1 * qstar + alpha2 * qnew + beta * dt * L( qstar )
// alpha1 = 1.0
// alpha2 = 0.0
// beta = 1.0
// ------------------------------------------------
// Stage #1
rk.mstage = 1;
dogStateUnst2.set_time(told);
BeforeStep_Unst(dt,Mesh,aux,qnew);
ConstructL_Unst(told, vel_vec,Mesh,EdgeData,aux,qnew,Lstar,smax);
Lold.copyfrom(Lstar);
UpdateSoln_Unst(rk.alpha1->get(rk.mstage),rk.alpha2->get(rk.mstage),
rk.beta->get(rk.mstage),dt,Mesh,aux,qnew,Lstar,qstar);
AfterStep_Unst(dt,Mesh,aux,qstar);
// -------------------------------------------------
// alpha1 = 0.75
// alpha2 = 0.25
// beta = 0.25
// Stage #2
rk.mstage = 2;
dogStateUnst2.set_time(told+0.5*dt);
BeforeStep_Unst(dt,Mesh,aux,qstar);
ConstructL_Unst(told+dt, vel_vec,Mesh,EdgeData,aux,qstar,Lstar,smax);
UpdateSoln_Unst(rk.alpha1->get(rk.mstage),rk.alpha2->get(rk.mstage),
rk.beta->get(rk.mstage),dt,Mesh,aux,qnew,Lstar,qstar);
AfterStep_Unst(dt,Mesh,aux,qstar);
// --------------------------------------------------
// alpha1 = 2/3
// alpha2 = 1/3
// beta = 2/3
// Stage #3
rk.mstage = 3;
dogStateUnst2.set_time(told+dt);
BeforeStep_Unst(dt,Mesh,auxstar,qstar);
ConstructL_Unst(told+0.5*dt,vel_vec,Mesh,EdgeData,auxstar,qstar,Lstar,smax);
UpdateSoln_Unst(rk.alpha1->get(rk.mstage),rk.alpha2->get(rk.mstage),
rk.beta->get(rk.mstage),dt,Mesh,aux,qstar,Lstar,qnew);
AfterStep_Unst(dt,Mesh,aux,qnew);
// --------------------------------------------------
break;
default: unsupported_value_error(dogParams.get_time_order());
}
// compute cfl number
cfl = GetCFL_Unst(dt,Mesh,aux,smax);
// output time step information
// if (dogParams.get_verbosity()>0)
// {
// printf(" In DogSolveRK_Quiet: DogSolve2D ... Step %5d"
// " CFL =%6.3f"
// " dt =%11.3e"
// " t =%11.3e\n",
// n_step, cfl, dt, t);
// }
// choose new time step
if (cfl>0.0)
{
dt = Min(dogParams.get_max_dt(), dt*CFL_target/cfl);
dtmin = Min(dt,dtmin);
dtmax = Max(dt,dtmax);
}
else
{
dt = dogParams.get_max_dt();
}
// see whether to accept or reject this step
if (cfl<=CFL_max)
// accept
{
m_accept = 1;
dogStateUnst2.set_time(t);
// do any extra work
// AfterFullTimeStep_Unst(dogStateUnst2.get_dt(),Mesh,
// auxold,qold,Lold,aux,qnew);
}
else
//reject
{
t = told;
dogStateUnst2.set_time(told);
// if( dogParams.get_verbosity() > 0 )
// {
// printf("DogSolve2D rejecting step..."
// "CFL number too large\n");
// }
// copy qold into qnew
qnew.copyfrom(qold);
aux.copyfrom(auxold);
// after reject function
// AfterReject_Unst(Mesh,dt,aux,qnew);
}
}
}
// printf(" Finished! t = %2.3e and nsteps = %d\n", t, n_step );
// set initial time step for next call to DogSolveRK
dogStateUnst2.set_initial_dt(dt);
void DeleteRKInfo(RKinfo& rk);
DeleteRKInfo(rk);
return cfl;
}