I have used LBM for some simulations, and I wanted to check convergence for a transient solution. I solved a Womersley flow in which a sinusoidal pressure wave is applied to a 2D channel. I have a solution to the Womersley problem by using Fourier Series. I now want to change grid size for my LBM solution and see how it converges. Starting out, I used a grid of nx=21 and ny=21. I specified Tau to fix the viscosity. I chose a value for Umax so that fpois could be calculated using the equation fpois=Umax8visc/nx/nx. I compare this to the Fourier solution and the results are very good. I now want to change the grid from ny=21 to ny=41. I want to check these results. How do I tweak the visc, Umax, tau etc. to handle a new grid of 41? I appreciate any help with this.
I stumbled across the solution…I divided the max velocity by 4 and multiplied the viscosity by 4. I will do my units when I get more time. The other peculiar thing involved the boundary conditions. For the grids 11, 21, and 41, the solution greatly improved in accuracy. However, when I went to the grid 81, there is a big jump at both wall boundaries from the exact solution! The convergence looked very nice until this grid. Can someone tell me why this numerical situation occurs? Thanks.
I bet that your numerical setup is wrong in the 81-case. There is no physical reason why this simultion should behave badly. For example: Does your boundary cover the entire side wall? I forgot a piece of the wall once, and the solution was bad. Maybe your boundaries are misplaced and shifted.