# Dirichlet B.C. with point source

Dear All:

I am trying to solve an advection equation where the boundary condition is given by a point source.


\partial_t\rho+\partial_x(u_x\rho)+\partial_y(u_y\rho)=\delta(x-0)\delta(y-0)



That is, at the boundary the nonzero density (\rho) appears only at the corner cell of the grid. I have tried filling the corner cell with the equilibrium distributions corresponding to \rho due to B.C. In the streaming step, I set the unknown distributions to be be zero. This is causing mass loss and also negative \rho coming from the boundary. Can anyone suggest how to implement this kind of boundary condition in LBM?

Thanks and regards

Andrew

Dear Andrew,

Don’t know if it works but try to use Zou-He boundaries or Inamuro.

Cheers,
Alex