PCDStokesCouette2D.cpp

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#include "Sundance.hpp"

#if defined(HAVE_SUNDANCE_EXODUS) && defined(Trilinos_DATA_DIR)


Array<double> runit(const string& meshName)
{
  VectorType<double> vecType = new EpetraVectorType();
  MeshType meshType = new BasicSimplicialMeshType();
  MeshSource mesher = new ExodusMeshReader(meshName, meshType);
  Mesh mesh = mesher.getMesh();

  BasisFamily P2 = new Lagrange(2);
  BasisFamily P1 = new Lagrange(1);
  QuadratureFamily quad = new GaussianQuadrature(4);

  Expr ux = new UnknownFunction(P2);
  Expr uy = new UnknownFunction(P2);
  Expr vx = new TestFunction(P2);
  Expr vy = new TestFunction(P2);
  Expr u = List(ux, uy);
  Expr v = List(vx, vy);

  Expr p = new UnknownFunction(P1);
  Expr q = new TestFunction(P1);

  CellFilter interior = new MaximalCellFilter();
  CellFilter sides = new DimensionalCellFilter(1);
  CellFilter pts = new DimensionalCellFilter(0);
  CellFilter peg = pts.labeledSubset(1);
  CellFilter inner = sides.labeledSubset(2);
  CellFilter outer = sides.labeledSubset(1);

  Expr grad = gradient(2);
  Expr x = new CoordExpr(0);
  Expr y = new CoordExpr(1);
  Expr r = sqrt(x*x+y*y);
  double uIn = 0.25;
  double uOut = 1.0;
  Expr uInnerX = -uIn*y/r;
  Expr uInnerY = uIn*x/r;
  Expr uOuterX = -uOut*y/r;
  Expr uOuterY = uOut*x/r;
  Expr uInner = List(uInnerX, uInnerY);
  Expr uOuter = List(uOuterX, uOuterY);

  Expr nu = 1.0;
  double C1 = 20.0;
  double C2 = 20.0;

  /* Stokes equations */
  Expr eqn = Integral(interior, 
    nu * colonProduct( outerProduct(grad, u), outerProduct(grad, v) ) 
    - p*div(v) - q*div(u), quad)
    + NitscheStokesNoSlipBC(inner, quad, nu, v, q, u, p, uInner, C1, C2)
    + NitscheStokesNoSlipBC(outer, quad, nu, v, q, u, p, uOuter, C1, C2);

  Expr dummyBC;

  /* Equations for the PCD preconditioner */
  Expr MpEqn = Integral(interior, p*q, quad);
  Expr ApEqn = Integral(interior, (grad*p)*(grad*q), quad) 
    + Integral(peg, p*q, quad);
  Expr FpEqn = Integral(interior, (grad*p)*(grad*q), quad) 
    + Integral(peg, p*q, quad);

  /* Arrange the variables into blocks: [velocity, pressure] */
  Array<Block> unkBlocks = tuple(Block(u, vecType), Block(p, vecType));
  Array<Block> varBlocks = tuple(Block(v, vecType), Block(q, vecType));

  /* Form the Stokes problem */
  LinearProblem prob( mesh , eqn , dummyBC , varBlocks, unkBlocks );

  /* Form the PCD problems */
  LinearProblem MpProb(mesh, MpEqn, dummyBC, q, p, vecType);
  LinearProblem ApProb(mesh, ApEqn, dummyBC, q, p, vecType);
  LinearProblem FpProb(mesh, FpEqn, dummyBC, q, p, vecType);

  /* Read the parameters. This is a little complicated because the
   * PCD precond parameters contain solver parameter lists */
  ParameterXMLFileReader outerSolverReader("pcd-outer-belos.xml");
  ParameterList outerSolverParams = outerSolverReader.getParameters();
  ParameterList precParams = outerSolverParams.sublist("PCD Preconditioner");
  LinearSolver<double> outerSolver = LinearSolverBuilder::createSolver(outerSolverParams);

  /* Form the preconditioner, and set it as a user preconditioner */
  PreconditionerFactory<double> outerPrec 
    = new PCDPreconditionerFactory(precParams, MpProb, ApProb, FpProb);
  outerSolver.setUserPrec(outerPrec);

  /* Solve the problem */
  Expr soln = prob.solve(outerSolver);

  /* Compare to the exact solution */

  double c1 = -2.0/3.0*(uIn-2.0*uOut);
  double c2 = 1.0/3.0*(2.0*uIn - uOut);
  Expr uMagExact = c1*r + c2/r;
  Expr uxExact = -uMagExact*y/r;
  Expr uyExact = uMagExact*x/r;
  Expr uExact = List(uxExact, uyExact);

  double area = L2Norm(mesh, interior, 1.0, quad);
  double uErrorNorm = L2Norm(mesh, interior, soln[0]-uExact, quad)/area;
  double pErrorNorm = L2Norm(mesh, interior, soln[1], quad)/area;


  Expr h = new CellDiameterExpr();
  double hAvg = L2Norm(mesh, interior, h, quad)/area;

  
  Out::root() << "average h = " << hAvg << std::endl;
  Out::root() << "velocity error norm = " << uErrorNorm << std::endl;
  Out::root() << "pressure error norm = " << pErrorNorm << std::endl;

    


  // project velocity onto P1
  DiscreteSpace P1Space( mesh , P1 , vecType );
  L2Projector proj_ux( P1Space , soln[0][0] );
  L2Projector proj_uy( P1Space , soln[0][1] );
  L2Projector proj_uxEx( P1Space , uxExact );
  L2Projector proj_uyEx( P1Space , uyExact );

  Expr ux_P1 = proj_ux.project( );
  Expr uy_P1 = proj_uy.project( );

  Expr uxEx_P1 = proj_uxEx.project( );
  Expr uyEx_P1 = proj_uyEx.project( );
    
  FieldWriter w = new VTKWriter("PCDStokes-" + meshName);
  w.addMesh(mesh);
  w.addField( "ux" , new ExprFieldWrapper( ux_P1 ) );
  w.addField( "uy" , new ExprFieldWrapper( uy_P1 ) );
  w.addField( "p" , new ExprFieldWrapper( soln[1] ) );
  w.addField( "uxEx" , new ExprFieldWrapper( uxEx_P1 ) );
  w.addField( "uyEx" , new ExprFieldWrapper( uyEx_P1 ) );
  w.write();

  return tuple<double>(hAvg, uErrorNorm, pErrorNorm);
}








int main( int argc , char **argv )
{
  try 
  {
    Sundance::init( &argc , &argv );

    Array<Array<double> > results;
    for (int n=0; n<=1; n++)
    {
      string meshName = "diskWithHole2D-" + Teuchos::toString(n);
      Array<double> x = runit(meshName);
      results.append(x);
    }

    for (int n=0; n<results.size(); n++)
    {
      Out::root() << setw(12) << results[n][0] << setw(20) << results[n][1]
                  << setw(20) << results[n][2] << endl;
    }

    Sundance::passFailTest(results[0][1], 0.001);
  }
  catch (exception &e) {
    Out::os() << e.what() << std::endl;
  }

  Sundance::finalize();
  return Sundance::testStatus(); 
}

    


#else


int main(int argc, char** argv)
{
  Sundance::init(&argc, &argv);
  std::cout << "dummy PCDStokes PASSED. Enable exodus to run the actual test" << std::endl;
  Sundance::finalize();
  return 0;
}


#endif    

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