void cavitySetup( MultiBlockLattice3D<T,DESCRIPTOR>& lattice,
IncomprFlowParam<T> const& parameters,
OnLatticeBoundaryCondition3D<T,DESCRIPTOR>& boundaryCondition )
{
const plint nx = parameters.getNx();
const plint ny = parameters.getNy();
const plint nz = parameters.getNz();
Box3D topLid = Box3D(0, nx-1, ny-1, ny-1, 0, nz-1);
Box3D bottomLid = Box3D(0, nx-1, 0, 0, 0, nz-1);
Box3D everythingButTopLid = Box3D(0, nx-1, 0, ny-2, 0, nz-1);
/*
instantiateOuterNLDboundary(lattice, lattice.getBoundingBox());
setOuterNLDboundaryDynamics(lattice, lattice.getBackgroundDynamics().clone(),
lattice.getBoundingBox(), boundary::dirichlet);
setOuterNLDboundaryDynamics(lattice, lattice.getBackgroundDynamics().clone(), bottomLid, boundary::neumann);
defineDynamics(lattice, bottomLid, lattice.getBackgroundDynamics().clone());
*/
boundaryCondition.setVelocityConditionOnBlockBoundaries(lattice, lattice.getBoundingBox(), boundary::dirichlet);
T u = sqrt((T)2)/(T)2 * parameters.getLatticeU();
initializeAtEquilibrium(lattice, everythingButTopLid, (T) 1., Array<T,3>(0.,0.,0.) );
initializeAtEquilibrium(lattice, topLid, (T) 1., Array<T,3>(u,0.,u) );
setBoundaryVelocity(lattice, topLid, Array<T,3>(u,0.,u) );
lattice.initialize();
}
void writeVTK(MultiBlockLattice2D<T,DESCRIPTOR>& lattice,
IncomprFlowParam<T> const& parameters, plint iter)
{
T dx = parameters.getDeltaX();
T dt = parameters.getDeltaT();
VtkImageOutput2D<T> vtkOut(createFileName("vtk", iter, 6), dx);
vtkOut.writeData<float>(*computeVelocityNorm(lattice), "velocityNorm", dx/dt);
vtkOut.writeData<2,float>(*computeVelocity(lattice), "velocity", dx/dt);
}
void writeVTK(BlockLatticeT& lattice,
IncomprFlowParam<T> const& parameters, plint iter)
{
T dx = parameters.getDeltaX();
T dt = parameters.getDeltaT();
VtkImageOutput3D<T> vtkOut(createFileName("vtk", iter, 6), dx);
vtkOut.writeData<float>(*computeVelocityNorm(lattice), "velocityNorm", dx/dt);
vtkOut.writeData<3,float>(*computeVelocity(lattice), "velocity", dx/dt);
vtkOut.writeData<3,float>(*computeVorticity(*computeVelocity(lattice)), "vorticity", 1./dt);
}
void velocityNeumannOutlet( MultiBlockLattice2D<T,DESCRIPTOR>& lattice,
IncomprFlowParam<T> const& parameters,
OnLatticeBoundaryCondition2D<T,DESCRIPTOR>& boundaryCondition )
{
const plint nx = parameters.getNx();
const plint ny = parameters.getNy();
boundaryCondition.addVelocityBoundary0P (
Box2D(nx-1,nx-1, 0,ny-1), lattice, boundary::outflow );
}
void copyUnknownOnOutlet( MultiBlockLattice2D<T,DESCRIPTOR>& lattice,
IncomprFlowParam<T> const& parameters,
OnLatticeBoundaryCondition2D<T,DESCRIPTOR>& boundaryCondition )
{
const plint nx = parameters.getNx();
const plint ny = parameters.getNy();
// On the right boundary, we copy the unknown populations from previous locations
integrateProcessingFunctional(new CopyUnknownPopulationsFunctional2D<T,DESCRIPTOR, 0, +1>,
Box2D(nx-1,nx-1, 0,ny-1), lattice);
}
void defineCylinderGeometry( MultiBlockLattice2D<T,DESCRIPTOR>& lattice,
IncomprFlowParam<T> const& parameters )
{
const plint nx = parameters.getNx();
const plint ny = parameters.getNy();
int cx = nx/4;
int cy = ny/2+ny/10;
int radius = cy/4;
createCylinder(lattice, cx, cy, radius);
}
/// A functional, used to instantiate bounce-back nodes at the locations of the cylinder
void cylinderSetup( MultiBlockLattice2D<T,DESCRIPTOR>& lattice,
IncomprFlowParam<T> const& parameters,
OnLatticeBoundaryCondition2D<T,DESCRIPTOR>& boundaryCondition )
{
const plint nx = parameters.getNx();
const plint ny = parameters.getNy();
Box2D outlet(nx-1,nx-1, 1,ny-2);
// Create Velocity boundary conditions everywhere
boundaryCondition.setVelocityConditionOnBlockBoundaries (
lattice, Box2D(0, nx-1, 0, 0) );
boundaryCondition.setVelocityConditionOnBlockBoundaries (
lattice, Box2D(0, nx-1, ny-1, ny-1) );
boundaryCondition.setVelocityConditionOnBlockBoundaries (
lattice, Box2D(0,0, 1,ny-2) );
// .. except on right boundary, where we prefer a fixed-pressure condition.
boundaryCondition.setPressureConditionOnBlockBoundaries (
lattice, outlet );
setBoundaryVelocity (
lattice, lattice.getBoundingBox(),
PoiseuilleVelocity<T>(parameters) );
setBoundaryDensity (
lattice, outlet,
ConstantDensity<T>(1.) );
initializeAtEquilibrium (
lattice, lattice.getBoundingBox(),
PoiseuilleVelocityAndDensity<T,DESCRIPTOR>(parameters) );
plint cx = nx/4;
plint cy = ny/2+2;
plint r = cy/4;
DotList2D cylinderShape;
for (plint iX=0; iX<nx; ++iX) {
for (plint iY=0; iY<ny; ++iY) {
if ( (iX-cx)*(iX-cx) + (iY-cy)*(iY-cy) < r*r ) {
cylinderShape.addDot(Dot2D(iX,iY));
}
}
}
defineDynamics(lattice, cylinderShape, new BounceBack<T,DESCRIPTOR>);
lattice.initialize();
}
void cavitySetup( MultiBlockLattice2D<T,DESCRIPTOR>& lattice,
IncomprFlowParam<T> const& parameters,
OnLatticeBoundaryCondition2D<T,DESCRIPTOR>& boundaryCondition )
{
const plint nx = parameters.getNx();
const plint ny = parameters.getNy();
boundaryCondition.setVelocityConditionOnBlockBoundaries(lattice);
setBoundaryVelocity(lattice, lattice.getBoundingBox(), Array<T,2>(0.,0.) );
initializeAtEquilibrium(lattice, lattice.getBoundingBox(), 1., Array<T,2>(0.,0.) );
T u = parameters.getLatticeU();
setBoundaryVelocity(lattice, Box2D(1, nx-2, ny-1, ny-1), Array<T,2>(u,0.) );
initializeAtEquilibrium(lattice, Box2D(1, nx-2, ny-1, ny-1), 1., Array<T,2>(u,0.) );
lattice.initialize();
}
/// Velocity on the parabolic Womersley profile
T womersleyVelocity(plint iY, T t, T A, T omega, T alpha, IncomprFlowParam<T> const& parameters)
{
const complex<T> I(0.,1.);
T y = (T)iY / parameters.getResolution();
return ( A / (I * omega) * std::exp(I * omega * t) *
( (T)1. - std::cosh(std::sqrt((T)2.)*(y-(T).5)*(alpha+I*alpha)) /
std::cosh(std::sqrt((T)2.)/(T)2. * (alpha+I*alpha)) ) ).real();
}
void writeGifs(BlockLatticeT& lattice,
IncomprFlowParam<T> const& parameters, plint iter)
{
const plint imSize = 600;
const plint nx = parameters.getNx();
const plint ny = parameters.getNy();
const plint nz = parameters.getNz();
const plint zComponent = 2;
Box3D slice(0, nx-1, 0, ny-1, nz/2, nz/2);
ImageWriter<T> imageWriter("leeloo");
imageWriter.writeScaledGif( createFileName("uz", iter, 6),
*computeVelocityComponent (lattice, slice, zComponent),
imSize, imSize );
imageWriter.writeScaledGif( createFileName("uNorm", iter, 6),
*computeVelocityNorm (lattice, slice),
imSize, imSize );
}
void cavitySetup( MultiBlockLattice3D<T,DESCRIPTOR>& lattice,
IncomprFlowParam<T> const& parameters,
OnLatticeBoundaryCondition3D<T,DESCRIPTOR>& boundaryCondition )
{
const plint nx = parameters.getNx();
const plint ny = parameters.getNy();
const plint nz = parameters.getNz();
Box3D topLid = Box3D(0, nx-1, ny-1, ny-1, 0, nz-1);
Box3D everythingButTopLid = Box3D(0, nx-1, 0, ny-2, 0, nz-1);
boundaryCondition.setVelocityConditionOnBlockBoundaries(lattice);
T u = std::sqrt((T)2)/(T)2 * parameters.getLatticeU();
initializeAtEquilibrium(lattice, everythingButTopLid, (T)1., Array<T,3>((T)0.,(T)0.,(T)0.) );
initializeAtEquilibrium(lattice, topLid, (T)1., Array<T,3>(u,(T)0.,u) );
setBoundaryVelocity(lattice, topLid, Array<T,3>(u,(T)0.,u) );
lattice.initialize();
}
/// A functional, used to instantiate bounce-back nodes at the locations of the cylinder
void cylinderSetup( BlockLatticeBase2D<T,DESCRIPTOR>& lattice,
IncomprFlowParam<T> const& parameters,
OnLatticeBoundaryCondition2D<T,DESCRIPTOR>& boundaryCondition )
{
const plint nx = parameters.getNx();
const plint ny = parameters.getNy();
Box2D outlet(nx-1,nx-1, 1, ny-2);
// Create Velocity boundary conditions everywhere
boundaryCondition.setVelocityConditionOnBlockBoundaries (
lattice, Box2D(0, 0, 1, ny-2) );
boundaryCondition.setVelocityConditionOnBlockBoundaries (
lattice, Box2D(0, nx-1, 0, 0) );
boundaryCondition.setVelocityConditionOnBlockBoundaries (
lattice, Box2D(0, nx-1, ny-1, ny-1) );
// .. except on right boundary, where we prefer an outflow condition
// (zero velocity-gradient).
boundaryCondition.setVelocityConditionOnBlockBoundaries (
lattice, Box2D(nx-1, nx-1, 1, ny-2), boundary::outflow );
setBoundaryVelocity (
lattice, lattice.getBoundingBox(),
PoiseuilleVelocity<T>(parameters) );
setBoundaryDensity (
lattice, outlet,
ConstantDensity<T>(1.) );
initializeAtEquilibrium (
lattice, lattice.getBoundingBox(),
PoiseuilleVelocityAndDensity<T>(parameters) );
plint cx = nx/4;
plint cy = ny/2+2; // cy is slightly offset to avoid full symmetry,
// and to get a Von Karman Vortex street.
plint radius = cy/4;
defineDynamics(lattice, lattice.getBoundingBox(),
new CylinderShapeDomain2D<T>(cx,cy,radius),
new plb::BounceBack<T,DESCRIPTOR>);
lattice.initialize();
}
int main(int argc, char* argv[]) {
plbInit(&argc, &argv);
global::directories().setOutputDir("./tmp/");
IncomprFlowParam<T> parameters (
(T) 1e-2, // uMax
(T) 10., // Re
30, // N
2., // lx
1. // ly
);
plint nx = parameters.getNx();
plint ny = parameters.getNy();
writeLogFile(parameters, "Poiseuille flow");
MultiBlockLattice2D<T, DESCRIPTOR> lattice (
nx, ny,
new BGKdynamics<T,DESCRIPTOR>(parameters.getOmega()) );
OnLatticeBoundaryCondition2D<T,DESCRIPTOR>*
boundaryCondition = createLocalBoundaryCondition2D<T,DESCRIPTOR>();
createPoiseuilleBoundaries(lattice, parameters, *boundaryCondition);
lattice.initialize();
// The following command opens a text-file, in which the velocity-profile
// in the middle of the channel will be written and several successive
// time steps. Note the use of plb_ofstream instead of the standard C++
// ofstream, which is required to guarantee a consistent behavior in MPI-
// parallel programs.
plb_ofstream successiveProfiles("velocityProfiles.dat");
// Main loop over time steps.
for (plint iT=0; iT<10000; ++iT) {
if (iT%1000==0) {
pcout << "At iteration step " << iT
<< ", the density along the channel is " << endl;
pcout << setprecision(7)
<< *computeDensity(lattice, Box2D(0, nx-1, ny/2, ny/2))
<< endl << endl;
Box2D profileSection(nx/2, nx/2, 0, ny-1);
successiveProfiles
<< setprecision(4)
// (2) Convert from lattice to physical units.
<< *multiply (
parameters.getDeltaX() / parameters.getDeltaT(),
// (1) Compute velocity norm along the chosen section.
*computeVelocityNorm (lattice, profileSection) )
<< endl;
}
// Lattice Boltzmann iteration step.
lattice.collideAndStream();
}
delete boundaryCondition;
}
void channelSetup( MultiBlockLattice2D<T,NSDESCRIPTOR>& lattice,
IncomprFlowParam<T> const& parameters,
OnLatticeBoundaryCondition2D<T,NSDESCRIPTOR>& boundaryCondition,
T alpha, T frequency, T amplitude)
{
const plint nx = parameters.getNx();
const plint ny = parameters.getNy();
Box2D bottom( 0,nx-1, 0, 0);
Box2D top( 0,nx-1, ny-1, ny-1);
boundaryCondition.addVelocityBoundary1N(bottom, lattice);
boundaryCondition.addPressureBoundary1P(top, lattice);
Array<T,2> u((T)0.,(T)0.);
setBoundaryVelocity( lattice, lattice.getBoundingBox(), u );
initializeAtEquilibrium(lattice,lattice.getBoundingBox(),(T)1.0,u);
Array<T,NSDESCRIPTOR<T>::d> force(womersleyForce((T)0, amplitude, frequency, parameters),0.);
setExternalVector(lattice,lattice.getBoundingBox(),NSDESCRIPTOR<T>::ExternalField::forceBeginsAt,force);
lattice.initialize();
}
void setupInletAndBulk( MultiBlockLattice2D<T,DESCRIPTOR>& lattice,
IncomprFlowParam<T> const& parameters,
OnLatticeBoundaryCondition2D<T,DESCRIPTOR>& boundaryCondition )
{
const plint ny = parameters.getNy();
// Create Velocity boundary conditions on inlet
boundaryCondition.addVelocityBoundary0N(Box2D( 0, 0, 0,ny-1), lattice);
setBoundaryVelocity (
lattice, Box2D( 0, 0, 0,ny-1),
PoiseuilleVelocity<T>(parameters) );
initializeAtEquilibrium (
lattice, lattice.getBoundingBox(),
PoiseuilleVelocityAndDensity<T,DESCRIPTOR>(parameters) );
}
T computeRMSerror ( MultiBlockLattice2D<T,NSDESCRIPTOR>& lattice,
IncomprFlowParam<T> const& parameters,
T alpha, plint iT, bool createImage=false)
{
MultiTensorField2D<T,2> analyticalVelocity(lattice);
setToFunction( analyticalVelocity, analyticalVelocity.getBoundingBox(),
WomersleyVelocity<T>(parameters,alpha,(T)iT) );
MultiTensorField2D<T,2> numericalVelocity(lattice);
computeVelocity(lattice, numericalVelocity, lattice.getBoundingBox());
// Divide by lattice velocity to normalize the error
return 1./parameters.getLatticeU() *
// Compute RMS difference between analytical and numerical solution
std::sqrt( computeAverage( *computeNormSqr (
*subtract(analyticalVelocity, numericalVelocity)
) ) );
}
/// Linearly decreasing pressure profile
T poiseuillePressure(plint iX, IncomprFlowParam<T> const& parameters) {
T Lx = parameters.getNx()-1;
T Ly = parameters.getNy()-1;
return 8.*parameters.getLatticeNu()*parameters.getLatticeU() / (Ly*Ly) * (Lx/(T)2-(T)iX);
}
/// Velocity on the parabolic Poiseuille profile
T poiseuilleVelocity(plint iY, IncomprFlowParam<T> const& parameters) {
T y = (T)iY / parameters.getResolution();
return 4.*parameters.getLatticeU() * (y-y*y);
}
