Пример #1
0
// 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 );
            }
    }

}
Пример #2
0
double GetCFL_Unst(double dt, const mesh& Mesh,
                   const dTensor3& aux, const dTensor1& smax)
{
    double cfl=-100.0;
    int NumPhysElems = Mesh.get_NumPhysElems();
    int NumEdges = Mesh.get_NumEdges();

    for (int i=1; i<=NumPhysElems; i++)
    {
        double Area  = Mesh.get_area_prim(i);
        int edge1 = Mesh.get_tedge(i,1);
        int edge2 = Mesh.get_tedge(i,2);
        int edge3 = Mesh.get_tedge(i,3);

        double tmp = Max(Max(smax.get(edge1),smax.get(edge2)),
                         smax.get(edge3));

        cfl = Max(0.5*dt*tmp/Area, cfl);
    }

    return cfl;
}
Пример #3
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) );
        }

    }

}
Пример #4
0
//
// 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");
}
Пример #5
0
// Right-hand side for hyperbolic PDE in divergence form
//
//       q_t = -( f(q,x,y,t)_x + g(q,x,y,t)_y ) + Psi(q,x,y,t)
//
void LaxWendroff_Unst(double dt,
    const mesh& Mesh, const edge_data_Unst& EdgeData,
    dTensor3& aux,                  // SetBndValues modifies ghost cells
    dTensor3& q,                    // SetBndValues modifies ghost cells
    dTensor3& Lstar, dTensor1& smax)
{

    const int NumElems      = Mesh.get_NumElems();
    const int NumPhysElems  = Mesh.get_NumPhysElems();
    const int NumEdges      = Mesh.get_NumEdges();
    const int meqn          = q.getsize(2);
    const int kmax          = q.getsize(3);
    const int maux          = aux.getsize(2);
    const int space_order   = dogParams.get_space_order();
    dTensor3 EdgeFluxIntegral(NumElems,meqn,kmax);
    dTensor3 ElemFluxIntegral(NumElems,meqn,kmax);
    dTensor3              Psi(NumElems,meqn,kmax);

    // ---------------------------------------------------------
    // Boundary Conditions
    SetBndValues_Unst(Mesh, &q, &aux);
    // ---------------------------------------------------------

    // --------------------------------------------------------------------- //
    // Part 0: Compute the Lax-Wendroff "flux" function:
    //
    // Here, we include the extra information about time derivatives.
    // --------------------------------------------------------------------- //
    dTensor3 F(NumElems, meqn, kmax );  F.setall(0.);
    dTensor3 G(NumElems, meqn, kmax );  G.setall(0.);
    L2ProjectLxW_Unst( dogParams.get_time_order(), 1.0, 0.5*dt, dt*dt/6.0, 1, NumElems,
        space_order, space_order, space_order, space_order, Mesh,
        &q, &aux, &F, &G, &FluxFunc, &DFluxFunc, &D2FluxFunc );

    // ---------------------------------------------------------
    // Part I: compute source term
    // --------------------------------------------------------- 
    if ( dogParams.get_source_term()>0 )
    {        
        // eprintf("error: have not implemented source term for LxW solver.");
        printf("Source term has not been implemented for LxW solver.  Terminating program.");
        exit(1);
    }
    Lstar.setall(0.);
    // ---------------------------------------------------------


    // ---------------------------------------------------------
    // Part II: compute flux integral on element edges
    // ---------------------------------------------------------

    // Loop over all interior edges
    EdgeFluxIntegral.setall(0.);
    ElemFluxIntegral.setall(0.);

#pragma omp parallel for
    // Loop over all interior edges
    for (int i=1; i<=NumEdges; i++)
    {
        // Edge coordinates
        double x1 = Mesh.get_edge(i,1);
        double y1 = Mesh.get_edge(i,2);
        double x2 = Mesh.get_edge(i,3);
        double y2 = Mesh.get_edge(i,4);

        // Elements on either side of edge
        int ileft  = Mesh.get_eelem(i,1);
        int iright = Mesh.get_eelem(i,2);  
        double Areal = Mesh.get_area_prim(ileft);
        double Arear = Mesh.get_area_prim(iright);

        // Scaled normal to edge
        dTensor1 nhat(2);      
        nhat.set(1, (y2-y1) );
        nhat.set(2, (x1-x2) );

        // Variables to store flux integrals along edge
        dTensor2 Fr_tmp(meqn,dogParams.get_space_order());
        dTensor2 Fl_tmp(meqn,dogParams.get_space_order());

        // Loop over number of quadrature points along each edge
        for (int ell=1; ell<=dogParams.get_space_order(); ell++)
        {
            dTensor1   Ql(meqn),   Qr(meqn);
            dTensor1  ffl(meqn),  ffr(meqn);  // << -- NEW PART -- >>
            dTensor1 Auxl(maux), Auxr(maux);

            // Riemann data - q
            for (int m=1; m<=meqn; m++)
            {
                Ql.set(m, 0.0 );
                Qr.set(m, 0.0 );

                // << -- NEW PART, ffl and ffr -- >> //
                ffl.set(m, 0.0 );
                ffr.set(m, 0.0 );

                for (int k=1; k<=kmax; k++)
                {
                    Ql.set(m, Ql.get(m) + EdgeData.phi_left->get(i,ell,k) 
                            *q.get(ileft, m,k) );
                    Qr.set(m, Qr.get(m) + EdgeData.phi_right->get(i,ell,k)
                            *q.get(iright,m,k) );

                    // << -- NEW PART, ffl and ffr -- >> //
                    // Is this the correct way to use the normal vector?
                    ffl.set(m, ffl.get(m) + EdgeData.phi_left->get (i, ell, k) * ( 
                        nhat.get(1)*F.get( ileft, m, k) + nhat.get(2)*G.get( ileft, m, k) ) );

                    ffr.set(m, ffr.get(m) + EdgeData.phi_right->get(i, ell, k) * (
                        nhat.get(1)*F.get(iright, m, k) + nhat.get(2)*G.get(iright, m, k) ) );

                }
            }

            // Riemann data - aux
            for (int m=1; m<=maux; m++)
            {
                Auxl.set(m, 0.0 );
                Auxr.set(m, 0.0 );

                for (int k=1; k<=kmax; k++)
                {
                    Auxl.set(m, Auxl.get(m) + EdgeData.phi_left->get(i,ell,k)  * aux.get(ileft, m,k) );
                    Auxr.set(m, Auxr.get(m) + EdgeData.phi_right->get(i,ell,k) * aux.get(iright,m,k) );
                }
            }

            // Solve Riemann problem
            dTensor1 xedge(2);
            double s = EdgeData.xpts1d->get(ell);
            xedge.set(1, x1 + 0.5*(s+1.0)*(x2-x1) );
            xedge.set(2, y1 + 0.5*(s+1.0)*(y2-y1) );

            // Solve the Riemann problem for this edge
            dTensor1 Fl(meqn), Fr(meqn);

            // Use the time-averaged fluxes to define left and right values for
            // the Riemann solver.
            const double smax_edge = RiemannSolveLxW(
                    nhat, xedge, Ql, Qr, Auxl, Auxr, ffl, ffr, Fl, Fr);
            smax.set(i, Max(smax_edge,smax.get(i)) );

            // Construct fluxes
            for (int m=1; m<=meqn; m++)
            {
                Fr_tmp.set(m,ell, Fr.get(m) );
                Fl_tmp.set(m,ell, Fl.get(m) );
            }
        }

        // Add edge integral to line integral around the full element
        for (int m=1; m<=meqn; m++)
        for (int k=1; k<=kmax; k++)
        {
            double Fl_sum = 0.0;
            double Fr_sum = 0.0;
            for (int ell=1; ell<=dogParams.get_space_order(); ell++)
            {
                Fl_sum = Fl_sum + 0.5*EdgeData.wgts1d->get(ell)
                    *EdgeData.phi_left->get(i,ell,k) *Fl_tmp.get(m,ell);
                Fr_sum = Fr_sum + 0.5*EdgeData.wgts1d->get(ell)
                    *EdgeData.phi_right->get(i,ell,k)*Fr_tmp.get(m,ell);
            }
            EdgeFluxIntegral.set(ileft, m,k, EdgeFluxIntegral.get(ileft, m,k) + Fl_sum/Areal );
            EdgeFluxIntegral.set(iright,m,k, EdgeFluxIntegral.get(iright,m,k) - Fr_sum/Arear );
        }
    }
    // ---------------------------------------------------------

    // ---------------------------------------------------------
    // Part III: compute intra-element contributions
    // ---------------------------------------------------------
    if( dogParams.get_space_order() > 1 )
    {
        L2ProjectGradAddLegendre_Unst(1, NumPhysElems, space_order, 
            Mesh, &F, &G, &ElemFluxIntegral );
    }
    // ---------------------------------------------------------

    // ---------------------------------------------------------
    // Part IV: construct Lstar
    // ---------------------------------------------------------
    if (dogParams.get_source_term()==0)  // Without Source Term
    { 
#pragma omp parallel for
        for (int i=1; i<=NumPhysElems; i++)	
        for (int m=1; m<=meqn; m++)
        for (int k=1; k<=kmax; k++)
        {
            double tmp = ElemFluxIntegral.get(i,m,k) - EdgeFluxIntegral.get(i,m,k);
            Lstar.set(i,m,k, tmp );	      
        }
    }
    else  // With Source Term
    {
#pragma omp parallel for
        for (int i=1; i<=NumPhysElems; i++)
        for (int m=1; m<=meqn; m++)
        for (int k=1; k<=kmax; k++)
        {
//          double tmp = ElemFluxIntegral.get(i,m,k) 
//              - EdgeFluxIntegral.get(i,m,k)
//              + Psi.get(i,m,k);

//          Lstar.set(i,m,k, tmp );

            printf("Source term has not been implemented for LxW solver.  Terminating program.");
            exit(1);
        }
    }
    // ---------------------------------------------------------

    // ---------------------------------------------------------
    // Part V: add extra contributions to Lstar
    // ---------------------------------------------------------
    // Call LstarExtra
    LstarExtra_Unst(Mesh, &q, &aux, &Lstar);
    // ---------------------------------------------------------

    // ---------------------------------------------------------
    // Part VI: artificial viscosity limiter
    // ---------------------------------------------------------  
//  if (dogParams.get_space_order()>1  &&
//          dogParams.using_viscosity_limiter())
//  {  ArtificialViscosity(&aux,&q,&Lstar);  }
    // ---------------------------------------------------------

}
// 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;

}
// This is the positivity preserving limiter proposed in 
// "Maximum-Principle-Satisfying and Positivity-Preserving
// High Order Discontinuous Galerkin Schemes
// for Conservation Laws on Triangular Meshes", Zhang, Xia and Shu
// J. Sci. Comput. (2012).
//
// THIS METHOD ASSUMES THAT EVERY COMPONENT OF CONSERVED VARIABLES SHOULD STAY
// POSITIVE.
//
// In order to implement this for a different scheme, one should rewrite, or
// redefine what components should remain positiive.  This will require
// reworking the control flow logic for how time step lengths are chosen.
void ApplyPosLimiter_Unst(const mesh& Mesh, const dTensor3& aux, dTensor3& q)
{

    const int NumElems      = Mesh.get_NumElems();
    const int NumPhysElems  = Mesh.get_NumPhysElems();
    const int NumEdges      = Mesh.get_NumEdges();
    const int meqn          = q.getsize(2);
    const int kmax          = q.getsize(3);
    const int maux          = aux.getsize(2);
    const int space_order   = dogParams.get_space_order();

    // Do nothing in the case of piecewise constants
    if( space_order == 1 )
    { return; }

    // ------------------------------------------------ //
    // number of points where we want to check solution //
    // ------------------------------------------------ //
    const int space_order_sq = space_order*space_order;
    const int mpts_vec[] = {0, 3*space_order_sq, 18, 3*space_order_sq, 3*space_order_sq };  // TODO - FILL IN 2ND-ORDER CASE
    const int mpoints    = mpts_vec[space_order-1];

    // ---------------------------------------------------------- //
    // sample basis at all points where we want to check solution //
    // ---------------------------------------------------------- //
    dTensor2 spts(mpoints, 2);
    void SetPositivePoints_Unst(const int& space_order, dTensor2& spts);
    SetPositivePoints_Unst(space_order, spts);

    void SamplePhiAtPositivePoints_Unst(const int& space_order, 
            const dTensor2& spts, dTensor2& phi);
    dTensor2 phi(mpoints, kmax);
    SamplePhiAtPositivePoints_Unst(space_order, spts, phi);

    // -------------------------------------------------------------- //
    // q_limited = Q1 + \theta ( q(xi,eta) - Q1 )                     //
    // where theta = min(1, |Q1| / |Q1-m|; m = min_{i} q(xi_i, eta_i) //
    // -------------------------------------------------------------- //
#pragma omp parallel for
    for(int  i=1;  i <= NumPhysElems; i++)
    for(int me=1; me <= meqn; me++)
    {

        double m = 0.0;
        for(int mp=1; mp <= mpoints; mp++)
        {
            // evaluate q at spts(mp) //
            double qnow = 0.0;
            for( int k=1; k <= kmax; k++ )
            {
                qnow += q.get(i,me,k) * phi.get(mp,k);
            }
            m = Min(m, qnow);
        }

        double theta = 0.0;
        double Q1 = q.get(i,me,1);  assert_ge( Q1, -1e-13 );
        if( fabs( Q1 - m ) < 1.0e-14 ){ theta = 1.0; }
        else{ theta = Min( 1.0, fabs( Q1 / (Q1 - m) ) ); }

        // limit q //
        for( int k=2; k <= kmax; k++ )
        {
            q.set(i,me,k, q.get(i,me,k) * theta );
        }

    }

}
Пример #8
0
// GAUSS-LOBATTO QUADRATURE ALONG EDGE
void SetEdgeDataGL_Unst(const mesh& Mesh, 
			int NumQuadPoints, 
			int NumBasisOrder, 
			edge_data_Unst* EdgeData)
{
  // Quick error check
  if (NumQuadPoints<2 || NumQuadPoints>6 || NumBasisOrder<1 || NumBasisOrder>5)
    {
      printf(" \n");
      printf(" Error in SetEdgeData_Unst.cpp \n");
      printf("   NumQuadPoints must be 2,3,4,5, or 6.\n");
      printf("   NumBasisOrder must be 1,2,3,4, or 5.\n");
      printf("     NumQuadPoints = %i\n",NumQuadPoints);
      printf("     NumBasisOrder = %i\n",NumBasisOrder);
      printf("\n");
      exit(1);
    }

  // ---------------------------------
  // Set quadrature weights and points
  // ---------------------------------
  switch( NumQuadPoints )
    {
    case 2:
      EdgeData->GL_wgts1d->set(1,  1.0 );
      EdgeData->GL_wgts1d->set(2,  1.0 );
      
      EdgeData->GL_xpts1d->set(1,  1.0 );
      EdgeData->GL_xpts1d->set(2, -1.0 );
      break;
      
    case 3:
      EdgeData->GL_wgts1d->set(1,  onethird );
      EdgeData->GL_wgts1d->set(2,  4.0*onethird );
      EdgeData->GL_wgts1d->set(3,  onethird );
      
      EdgeData->GL_xpts1d->set(1,  1.0 );
      EdgeData->GL_xpts1d->set(2,  0.0 );
      EdgeData->GL_xpts1d->set(3, -1.0 );
      break;
      
    case 4:
      EdgeData->GL_wgts1d->set(1,  0.5*onethird );
      EdgeData->GL_wgts1d->set(2,  2.5*onethird );
      EdgeData->GL_wgts1d->set(3,  2.5*onethird );
      EdgeData->GL_wgts1d->set(4,  0.5*onethird );
      
      EdgeData->GL_xpts1d->set(1,  1.0  );
      EdgeData->GL_xpts1d->set(2,  osq5 );
      EdgeData->GL_xpts1d->set(3, -osq5 );
      EdgeData->GL_xpts1d->set(4, -1.0  );
      break;
      
    case 5:
      EdgeData->GL_wgts1d->set(1,  0.1  );
      EdgeData->GL_wgts1d->set(2,  49.0/90.0 );
      EdgeData->GL_wgts1d->set(3,  32.0/45.0 );
      EdgeData->GL_wgts1d->set(4,  49.0/90.0 );
      EdgeData->GL_wgts1d->set(5,  0.1 );
      
      EdgeData->GL_xpts1d->set(1,  1.0      );
      EdgeData->GL_xpts1d->set(2,  sq3*osq7 );
      EdgeData->GL_xpts1d->set(3,  0.0      );
      EdgeData->GL_xpts1d->set(4, -sq3*osq7 );
      EdgeData->GL_xpts1d->set(5, -1.0      );        
      break;
      
    case 6:      
      EdgeData->GL_wgts1d->set(1,  0.2*onethird  );
      EdgeData->GL_wgts1d->set(2,  (1.4 - 0.1*sq7)*onethird );
      EdgeData->GL_wgts1d->set(3,  (1.4 + 0.1*sq7)*onethird );
      EdgeData->GL_wgts1d->set(4,  (1.4 + 0.1*sq7)*onethird );
      EdgeData->GL_wgts1d->set(5,  (1.4 - 0.1*sq7)*onethird );
      EdgeData->GL_wgts1d->set(6,  0.2*onethird );
      
      EdgeData->GL_xpts1d->set(1,  1.0                           );
      EdgeData->GL_xpts1d->set(2,  (1/21.0)*sqrt(147.0+42.0*sq7) );
      EdgeData->GL_xpts1d->set(3,  (1/21.0)*sqrt(147.0-42.0*sq7) );
      EdgeData->GL_xpts1d->set(4, -(1/21.0)*sqrt(147.0-42.0*sq7) );
      EdgeData->GL_xpts1d->set(5, -(1/21.0)*sqrt(147.0+42.0*sq7) );
      EdgeData->GL_xpts1d->set(6, -1.0                           );
      break;
    }

  // ---------------------------------
  // Legendre basis functions on the 
  // left and right of each edge
  // ---------------------------------
  const int NumEdges = Mesh.get_NumEdges();
  const int NumBasisComps = (NumBasisOrder*(NumBasisOrder+1))/2;
  dTensor1 xp1(3);
  dTensor1 yp1(3);
  dTensor1 xp2(3);
  dTensor1 yp2(3);
  dTensor1 xy1(2);
  dTensor1 xy2(2);
  dTensor1 mu1(NumBasisComps);
  dTensor1 mu2(NumBasisComps);

  for (int i=1; i<=NumEdges; i++)
    {   
      // Get edge information
      const double x1 = Mesh.get_edge(i,1);
      const double y1 = Mesh.get_edge(i,2);
      const double x2 = Mesh.get_edge(i,3);
      const double y2 = Mesh.get_edge(i,4);
      
      const int e1 = Mesh.get_eelem(i,1);
      const int e2 = Mesh.get_eelem(i,2);

      // Get element information about
      // the two elements that meet at
      // the current edge
      const double Area1 = Mesh.get_area_prim(e1);
      const double Area2 = Mesh.get_area_prim(e2);

      for (int k=1; k<=3; k++)
	{
	  xp1.set(k, Mesh.get_node(Mesh.get_tnode(e1,k),1) );
	  yp1.set(k, Mesh.get_node(Mesh.get_tnode(e1,k),2) );

	  xp2.set(k, Mesh.get_node(Mesh.get_tnode(e2,k),1) );
	  yp2.set(k, Mesh.get_node(Mesh.get_tnode(e2,k),2) );
	}

      const double xc1 = (xp1.get(1) + xp1.get(2) + xp1.get(3))/3.0;
      const double yc1 = (yp1.get(1) + yp1.get(2) + yp1.get(3))/3.0;
      const double xc2 = (xp2.get(1) + xp2.get(2) + xp2.get(3))/3.0;
      const double yc2 = (yp2.get(1) + yp2.get(2) + yp2.get(3))/3.0;

      // quadrature points on the edge
      for (int m=1; m<=NumQuadPoints; m++)
	{
	  // Take integration point s (in [-1,1])
	  // and map to physical domain
	  const double s = EdgeData->GL_xpts1d->get(m);
	  const double x = x1 + 0.5*(s+1.0)*(x2-x1);
	  const double y = y1 + 0.5*(s+1.0)*(y2-y1);

	  // Take physical point (x,y)
	  // and map into the coordinates
	  // of the two triangles that are
	  // adjacent to the current edge
	  xy1.set(1, ((yp1.get(3)-yp1.get(1))*(x-xc1) 
		    + (xp1.get(1)-xp1.get(3))*(y-yc1))/(2.0*Area1) );
	  xy1.set(2, ((yp1.get(1)-yp1.get(2))*(x-xc1) 
		    + (xp1.get(2)-xp1.get(1))*(y-yc1))/(2.0*Area1) );
	  
	  xy2.set(1, ((yp2.get(3)-yp2.get(1))*(x-xc2) 
		    + (xp2.get(1)-xp2.get(3))*(y-yc2))/(2.0*Area2) );
	  xy2.set(2, ((yp2.get(1)-yp2.get(2))*(x-xc2) 
		    + (xp2.get(2)-xp2.get(1))*(y-yc2))/(2.0*Area2) );

	  // Evaluate monomials at locations xy1
	  double xi = xy1.get(1);
	  double xi2 = xi*xi;
	  double xi3 = xi*xi2;
	  double xi4 = xi*xi3;

	  double eta = xy1.get(2);
	  double eta2 = eta*eta;
	  double eta3 = eta*eta2;
	  double eta4 = eta*eta3;

	  switch( NumBasisOrder )
	    {
	    case 5:  // fifth order		    		    
	      mu1.set(15, eta4     );
	      mu1.set(14, xi4      );
	      mu1.set(13, xi2*eta2 );
	      mu1.set(12, eta3*xi  );
	      mu1.set(11, xi3*eta  );
	      
	    case 4:  // fourth order
	      mu1.set(10, eta3     );
	      mu1.set(9,  xi3      );
	      mu1.set(8,  xi*eta2  );
	      mu1.set(7,  eta*xi2  );
	      
	    case 3:  // third order
	      mu1.set(6,  eta2     );
	      mu1.set(5,  xi2      );
	      mu1.set(4,  xi*eta   );		    
	      
	    case 2:  // second order		    
	      mu1.set(3, eta       );
	      mu1.set(2, xi        );
	      
	    case 1:  // first order
	      mu1.set(1, 1.0       );
	      
	      break;		    
	    }
	  
	  // Evaluate monomials at locations xy2
	  xi = xy2.get(1);
	  xi2 = xi*xi;
	  xi3 = xi*xi2;
	  xi4 = xi*xi3;
	  
	  eta = xy2.get(2);
	  eta2 = eta*eta;
	  eta3 = eta*eta2;
	  eta4 = eta*eta3;

	  switch( NumBasisOrder )
	    {
	    case 5:  // fifth order		    		    
	      mu2.set(15, eta4     );
	      mu2.set(14, xi4      );
	      mu2.set(13, xi2*eta2 );
	      mu2.set(12, eta3*xi  );
	      mu2.set(11, xi3*eta  );
	      
	    case 4:  // fourth order
	      mu2.set(10, eta3     );
	      mu2.set(9,  xi3      );
	      mu2.set(8,  xi*eta2  );
	      mu2.set(7,  eta*xi2  );
	      
	    case 3:  // third order
	      mu2.set(6,  eta2     );
	      mu2.set(5,  xi2      );
	      mu2.set(4,  xi*eta   );		    
	      
	    case 2:  // second order		    
	      mu2.set(3, eta       );
	      mu2.set(2, xi        );
	      
	    case 1:  // first order
	      mu2.set(1, 1.0       );
	      
	      break;		    
	    }
	  
	  // Finally, convert monomials to Legendre Polys
	  // on the two adjacent triangle
	  for (int k=1; k<=NumBasisComps; k++)
	    {
	      double tmp1 = 0.0;
	      double tmp2 = 0.0;
	      for (int j=1; j<=k; j++)
		{  
		  tmp1 = tmp1 + Mmat[k-1][j-1]*mu1.get(j);
		  tmp2 = tmp2 + Mmat[k-1][j-1]*mu2.get(j);
		}
	      
	      EdgeData->GL_phi_left->set(i,m,k,  tmp1 );
	      EdgeData->GL_phi_right->set(i,m,k, tmp2 );
	    }
	}
    }
  
}
Пример #9
0
void ConstructL_Unst(
    const double t,
    const dTensor2* vel_vec,
    const mesh& Mesh,
    const edge_data_Unst& EdgeData,
    dTensor3& aux, // SetBndValues_Unst modifies ghost cells
    dTensor3& q,   // SetBndValues_Unst modifies ghost cells
    dTensor3& Lstar, 
    dTensor1& smax)
{

    const int NumElems      = Mesh.get_NumElems();
    const int NumPhysElems  = Mesh.get_NumPhysElems();
    const int NumEdges      = Mesh.get_NumEdges();
    const int meqn          = q.getsize(2);
    const int kmax          = q.getsize(3);
    const int maux          = aux.getsize(2);
    const int space_order   = dogParams.get_space_order();

    dTensor3 EdgeFluxIntegral(NumElems,meqn,kmax);
    dTensor3 ElemFluxIntegral(NumElems,meqn,kmax);
    dTensor3              Psi(NumElems,meqn,kmax);


    // ---------------------------------------------------------
    // Boundary Conditions
    SetBndValues_Unst(Mesh,&q,&aux);  
    
    // Positivity limiter
    void ApplyPosLimiter_Unst(const mesh& Mesh, const dTensor3& aux, dTensor3& q);
    if( dogParams.using_moment_limiter() )
    { ApplyPosLimiter_Unst(Mesh, aux, q); }
    // ---------------------------------------------------------

    // ---------------------------------------------------------
    // Part I: compute flux integral on element edges
    // ---------------------------------------------------------

    // Loop over all interior edges and solve Riemann problems
    // dTensor1 nvec(2);

    // Loop over all interior edges
    EdgeFluxIntegral.setall(0.);
    ElemFluxIntegral.setall(0.);

    // Loop over all interior edges
#pragma omp parallel for
    for (int i=1; i<=NumEdges; i++)
    {
        // Edge coordinates
        double x1 = Mesh.get_edge(i,1);
        double y1 = Mesh.get_edge(i,2);
        double x2 = Mesh.get_edge(i,3);
        double y2 = Mesh.get_edge(i,4);

        // Elements on either side of edge
        int ileft  = Mesh.get_eelem(i,1);
        int iright = Mesh.get_eelem(i,2);  
        double Areal = Mesh.get_area_prim(ileft);
        double Arear = Mesh.get_area_prim(iright);

        // Scaled normal to edge
        dTensor1 nhat(2);      
        nhat.set(1, (y2-y1) );
        nhat.set(2, (x1-x2) );

        // Variables to store flux integrals along edge
        dTensor2 Fr_tmp(meqn,dogParams.get_space_order());
        dTensor2 Fl_tmp(meqn,dogParams.get_space_order());

        // Loop over number of quadrature points along each edge
        for (int ell=1; ell<=dogParams.get_space_order(); ell++)
        {
            dTensor1 Ql(meqn),Qr(meqn);
            dTensor1 Auxl(maux),Auxr(maux);	  

            // Riemann data - q
            for (int m=1; m<=meqn; m++)
            {
                Ql.set(m, 0.0 );
                Qr.set(m, 0.0 );

                for (int k=1; k<=kmax; k++)
                {
                    Ql.set(m, Ql.get(m) + EdgeData.phi_left->get(i,ell,k) 
                            *q.get(ileft, m,k) );
                    Qr.set(m, Qr.get(m) + EdgeData.phi_right->get(i,ell,k)
                            *q.get(iright,m,k) );
                }

            }


            // Riemann data - aux
            for (int m=1; m<=maux; m++)
            {
                Auxl.set(m, 0.0 );
                Auxr.set(m, 0.0 );

                for (int k=1; k<=kmax; k++)
                {
                    Auxl.set(m, Auxl.get(m) + EdgeData.phi_left->get(i,ell,k)
                            *aux.get(ileft, m,k) );
                    Auxr.set(m, Auxr.get(m) + EdgeData.phi_right->get(i,ell,k)
                            *aux.get(iright,m,k) );
                }
            }

            // Solve Riemann problem
            dTensor1 xedge(2);
            double s = EdgeData.xpts1d->get(ell);
            xedge.set(1, x1 + 0.5*(s+1.0)*(x2-x1) );
            xedge.set(2, y1 + 0.5*(s+1.0)*(y2-y1) );
            dTensor1 Fl(meqn),Fr(meqn);
            const double smax_edge = RiemannSolve(vel_vec, nhat, xedge, Ql, Qr, Auxl, Auxr, Fl, Fr);
            smax.set(i, Max(smax_edge,smax.get(i)) );

            // Construct fluxes
            for (int m=1; m<=meqn; m++)
            {
                Fr_tmp.set(m,ell, Fr.get(m) );
                Fl_tmp.set(m,ell, Fl.get(m) );
            }
        }

        // Add edge integral to line integral around the full element
        for (int m=1; m<=meqn; m++)
        for (int k=1; k<=kmax; k++)
        {
            double Fl_sum = 0.0;
            double Fr_sum = 0.0;
            for (int ell=1; ell<=dogParams.get_space_order(); ell++)
            {
                Fl_sum = Fl_sum + 0.5*EdgeData.wgts1d->get(ell)
                    *EdgeData.phi_left->get(i,ell,k) *Fl_tmp.get(m,ell);
                Fr_sum = Fr_sum + 0.5*EdgeData.wgts1d->get(ell)
                    *EdgeData.phi_right->get(i,ell,k)*Fr_tmp.get(m,ell);
            }
            EdgeFluxIntegral.set(ileft, m,k, EdgeFluxIntegral.get(ileft, m,k) + Fl_sum/Areal );
            EdgeFluxIntegral.set(iright,m,k, EdgeFluxIntegral.get(iright,m,k) - Fr_sum/Arear );
        }
    }
    // ---------------------------------------------------------

    // ---------------------------------------------------------
    // Part II: compute intra-element contributions
    // ---------------------------------------------------------
    L2ProjectGrad_Unst(vel_vec, 1,NumPhysElems,
            space_order,space_order,space_order,space_order,
            Mesh,&q,&aux,&ElemFluxIntegral,&FluxFunc);
    // ---------------------------------------------------------

    // ---------------------------------------------------------
    // Part III: compute source term
    // --------------------------------------------------------- 
    if ( dogParams.get_source_term()>0 )
    {        
        // Set source term on computational grid
        // Set values and apply L2-projection
        L2Project_Unst(t, vel_vec, 1,NumPhysElems,
                space_order,space_order,space_order,space_order,
                Mesh,&q,&aux,&Psi,&SourceTermFunc);
    }
    // ---------------------------------------------------------

    // ---------------------------------------------------------
    // Part IV: construct Lstar
    // ---------------------------------------------------------
    if (dogParams.get_source_term()==0)  // Without Source Term
    { 
#pragma omp parallel for
        for (int i=1; i<=NumPhysElems; i++)	
        for (int m=1; m<=meqn; m++)
        for (int k=1; k<=kmax; k++)
        {
            double tmp = ElemFluxIntegral.get(i,m,k) - EdgeFluxIntegral.get(i,m,k);
            Lstar.set(i,m,k, tmp );	      
        }
    }
    else  // With Source Term
    {
#pragma omp parallel for
        for (int i=1; i<=NumPhysElems; i++)
        for (int m=1; m<=meqn; m++)
        for (int k=1; k<=kmax; k++)
        {
            double tmp = ElemFluxIntegral.get(i,m,k) 
                - EdgeFluxIntegral.get(i,m,k)
                + Psi.get(i,m,k);

            Lstar.set(i,m,k, tmp );
        }
    }
    // ---------------------------------------------------------

    // ---------------------------------------------------------
    // Part V: add extra contributions to Lstar
    // ---------------------------------------------------------
    // Call LstarExtra
    LstarExtra_Unst(Mesh,&q,&aux,&Lstar);
    // ---------------------------------------------------------

}