Problem in calculating v-velocity in D2Q9 model

Lattice Boltzmann Method LBM: Theory
#1

Hi,

I’m trying to implement the D2Q9 model to simulate pressure driven Poiseuille flow. Though the formulations in the code are correct, I’m getting wrong contours for the v-velocity alone. This also results in non-conservation of continuity.

Kindly help out. Your help is really appreciated.

aswathy

#2

Hi aswathynairk
How did you undrestand that continuity can not be conserved??!!
Do you use any benchmark solution and compare your desults??
May be your relaxation time has not choose suitable

#3

Hi SA,

I calculated the divergence of the flow. Since my flow is incompressible, divergence essentially gives the idea about the continuity of the flow. So, the values I’m obtaining for del.v is significant i.e. of the order of 10^-3 ~ 10^ -4.

I also tried it for different relaxation times. It doesn’t result in lowering my continuity values.

aswathy

#4

Hi,

Are you caculating the divergence of the velocity field only? To have continuity the divergence of rho*V should be zero. For the Poiseuille flow in LBM formulation, the density is varying, and thus, divergence of the velocity should also be non-zero to compensate for this.
The Poiseuille flow is driven by a pressure gradient along the channel. Since p = cs^2 * rho and the lattice sound speed is a constant, there is also a density gradient.

Hope this helps.

Elrohir