Hi

I am a beginner and this(2D Driven square cavity problem) is of my first problem that I am solving. I have seen in one paper during computing "Deltax" and "Deltay" grid spacings on a cartesian-aligned square grid, second order central differencing used for interior points and second-order one sided differencing used for boundary points.

My question is what is the advantage of using different differencings. In my opinion if we were using uniform grid then grid spacing should be same all over the domain.Am I correct ? If I am wrong then what are the advantages of above differencings ?

If there are any books relating this type of problems please refer me.Thanks in advance.

rvndr

What method do you use? What code or package do you use?

oh ! I am sorry, the question is incomplete. I am using vorticity stream function formulation. I am not using any package. I didn't understand what do you mean by "what code ?" I am writing code in C.

Thanks for the reply.

As Re increases, you want to pack your mesh close to the moving boundary as finer mesh is required to resolve the gradients. It's more expensive computationally to use uniform mesh in this case, not really a big deal in 2d, but logically significant in the real world.

For the classic 2D driven cavity problem, you should probably refer the paper, by Ghia et al. " High-Re solutions for Incompressible Flow using the Navier-Stokes equations and a multigrid method", J. of Comp. Physics, 48,387-411 (1982).

As to using a different scheme at the boundaries, Eg. Central difference requires requires i+1 and i-1 points for solving du/dx. In that case you do not have i-1 at the boundary. Hence you use one sided differencing. An alternative is using a ghost cell method.

Also Refer Computational Fluid mechanics and Heat Transfer by Tannehill, might be helpful

Thanks reni ! could you give me the link to download that paper. I tried a lot but able to get only abstract of that paper.That will be a great help to me.Once more thanks in advance

rvndr

sorry the paper is available with the journal, so you would have to get it from a library or somewhere else.