# Flow around square cylinder is trouble with relaxation parameter

Hi dear all, i have a LBM solver which is developed for flow around square cylinders. Im trying to validate my code. I used Momemtum exchange method for validating before. But i couldnt obtain correct values. Then i decided to calculate CD with simple logic. Firstly, im calculating drag force due to pressure and secondly im calculating drag force due to viscosity. In this way, i obtained aproximate values with validation case. However, my error percentage is not enough, is about %6-10. For example, my Cd is 1.57, but in the validation case cd is 1.49. Im thinking this difference is caused by relaxation parameter and boundary conditions. I read some paper about relaxation parameter for first order bounce-back. It says omega should close to 2 enough. Do you have any idea how can i improve my accuracy. Or what is common mistakes for cases like mine. My code Re=100, omega = 1.7, u=0.05, and Cd=1.57 ( but in validation case 1.49), iteration 250000. Thank you

The drag is very dependent on the size of your domain at low Reynolds number. Did you try to vary it?

Thank you for responding. As i see from my attempts to validate, the reason of the errors are not relaxation parameters. Yes, there is no difference between the size of domains. My domain is exactly same with the validation case domain. I have an idea here, the corner problem of the square cylinder may be cause this differerence. Dou you have any experience or information about corner problems? In my code, the corners have two bounce-back B.C. For example, top-left corner has not only east-bounce back boundary condition but also south bounce back boundary condition. The error might be caused by this?

You are using bounce back on the cylinder then you have to take into account that the wall is located exactly in the middle between the last fluid node and the first BB node. So if you have say 10 lattice nodes in your cylinder it means it has size 11 for maximal accuracy.

Aah, thank you. This is my first mistake. I fix this mistake in the code. Then, I have exactly correct values at Re=40 which is steady flow. On the other hand, At Re=60 and Re=100 which is unsteady , the error is getting bigger with increasing Reynolds (unsteadiness increase). the error is 5 percent at Re=60, and 9 percent at Re=100. I think, this is regarding with the corner bounce back B.C. Do you have any article with that? Or can you give simple explanation to me about that, if you have any knowledge on it.

I donâ€™t think the problem is the corner. What happens when you increase the resolution?

Cd is constant after a certain resolution as we expect. The code uses the SRT. The problem migh be that?

I think the problem is that when you do not resolve your simulation enough there are numerical instabilities. You may want to use more stable collision models, like MRT or CompleteRegularized ones.