# poiseuille flow: problems

Hi All,

I was trying out some palabos feature and I tried to simulate poiseuille flow in a channell without following the palabos tutorial. Basically I imposed a velocity in the inlet-outlet walls and a bouce back dynamic on the top and bottom wall. It should be straight forward but gives me strange results.

Here the code:

[code=“cpp”]
#include
#include “palabos2D.h”
#include “palabos2D.hh”

using namespace std;
using namespace plb;

typedef double T;

#define NSDES descriptors::D2Q9Descriptor

int main(int argc, char *argv[])
{
// Init simulation
plbInit(&argc, &argv);

``````// Set omegas and constant velocity
const T nsOmega = 1.0;
Array<T,2> u0(1.0,0.0);

// Allocate lattice
MultiBlockLattice2D<T, NSDES> nsLattice(100, 10, new BGKdynamics<T, NSDES>(nsOmega));

// Create box2D for the boundaries
const plint nx = nsLattice.getNx();
const plint ny = nsLattice.getNy();

Box2D topWall(0, nx,    ny-1,ny);
Box2D bottomWall(0,nx,  0,1);
Box2D inlet(0,1,     1,ny -1);
Box2D outlet(nx-1,nx, 1,ny-1);

// Boundary conditions for NS dynamics
OnLatticeBoundaryCondition2D<T, NSDES> *nsBC = createLocalBoundaryCondition2D<T, NSDES>();

// Set the boundary conditions type
nsBC->setVelocityConditionOnBlockBoundaries(nsLattice, inlet);
nsBC->setVelocityConditionOnBlockBoundaries(nsLattice, outlet);

defineDynamics(nsLattice, topWall, new BounceBack<T, NSDES>);
defineDynamics(nsLattice, bottomWall, new BounceBack<T, NSDES>);

// Set the velocity value
setBoundaryVelocity(nsLattice, inlet, u0);
setBoundaryVelocity(nsLattice, outlet, u0);

// Init lattice
initializeAtEquilibrium(nsLattice, nsLattice.getBoundingBox(), 1.0, u0);
nsLattice.initialize();

//Write first image
ImageWriter<T> image("leeloo");
image.writeScaledGif(createFileName("vel",1,1), *computeVelocityNorm(nsLattice), nx,ny);

// Main LBM cycle
for (plint iT=0; iT < 10000; ++iT) {

if(iT%100==0) {
pcout << "Writing GIF...";
image.writeScaledGif(createFileName("vel",iT,2), *computeVelocityNorm(nsLattice), nx,ny);
}
nsLattice.collideAndStream();
}

pcout << "Hello palabos";
return 0;
``````

}

Any suggestions? Is there smth wrong with the code?

Hi sdea,

This isn’t Poiseuille flow! Poiseuille flow is the flow that develops when you apply a constant pressure difference across a channel or a pipe, which gives a parabolic velocity profile over the flow cross-section. To implement this kind of flow in a lattice Boltzmann simulation, you need to either apply a density difference between the inlet and outlet (using a higher value at the inlet) or apply a constant force on the fluid throughout the system and use periodic boundaries at the inlet and outlet.

If you want to apply constant velocity to the entire system, you cannot use no-slip (bounce back) boundaries at the top and bottom: you will probably need to make these periodic or constant velocity boundaries.

Regards,

Michael

Dear sdea,

even though you probably have solved the problem by now, here are some more hints on what went wrong in your code.

First, the velocity you are using for both boundary and initial condition of your simulation is too high. The velocity that is used here is not the physical one but the one in lattice units. Thus, to satisfy the LBMs inherent low Mach number condition the velocity must be small. People often restrict themselves to using u0<0.1, for example u0=0.001.

Additionally, the domains you are using to initiate the boundaries are too big. The way its done in your code snippet leads to boundaries that are each two cells wide. To prevent this, the domains should look as follows:

[code=“cpp”]
Box2D topWall (0, nx-1, ny-1, ny-1 );
Box2D bottomWall (0 , nx-1, 0, 0 );
Box2D inlet (0, 0, 1, ny-2 );
Box2D outlet (nx-1, nx-1, 1, ny-2);

``````

Applying these changes renders your code stable.

Hope this helps.

Regards,

kk``````