SundanceNitscheBC.cpp

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//                             Sundance
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#include "SundanceNitscheBC.hpp"
#include "SundanceIntegral.hpp"
#include "SundanceCellFilter.hpp"
#include "SundanceQuadratureFamily.hpp"
#include "SundanceVectorCalculus.hpp"
#include "SundanceCellVectorExpr.hpp"
#include "SundanceCellDiameterExpr.hpp"

namespace Sundance
{

Expr NitschePoissonDirichletBC(int dim,
  const CellFilter& cells,
  const QuadratureFamily& quad,
  const Expr& kappa,
  const Expr& v,
  const Expr& u,
  const Expr& uBC,
  const double& gamma)
{
  Expr grad = gradient(dim);
  Expr n = CellNormalExpr(dim,"n");
  Expr h = new CellDiameterExpr();

  return Integral(cells, -kappa*(v*((n*grad)*u) + (u-uBC)*((n*grad)*v))
    + gamma/h * v*(u-uBC), quad);
}

Expr NitscheStokesNoSlipBC(const CellFilter& cells,
  const QuadratureFamily& quad,
  const Expr& nu,
  const Expr& v,
  const Expr& q,
  const Expr& u,
  const Expr& p,
  const Expr& uBC,
  const double& gamma1,
  const double& gamma2
  )
{
  TEUCHOS_TEST_FOR_EXCEPT(nu.size() != 1);
  TEUCHOS_TEST_FOR_EXCEPT(v.size() != u.size());
  TEUCHOS_TEST_FOR_EXCEPT(uBC.size() != u.size());

  int dim = uBC.size();

  Expr grad = gradient(dim);
  Expr n = CellNormalExpr(dim,"n");
  Expr h = new CellDiameterExpr();
  
  return Integral(cells,
    -nu*(v*((n*grad)*u /*- (n*grad)*uBC*/) + (u-uBC)*((n*grad)*v))
    + p*(v*n) + q*((u-uBC)*n)
    + gamma1/h * v*(u-uBC) + gamma2/h * (v*n) * ((u-uBC)*n),
    quad);
}



}