hi all,

I have written a 2D finite volume steady incompressible Navier-Stokes code for lid driven cavity problem. I observed that at Re=100, it gives accurate results for 50*50 grid. But if I increase the number of grid points, it behaves with increased numerical viscosity (max u velocity at the centreline keeps on reducing as I increase the number of grids). I have used central differencing scheme for both convective and diffusive terms. can any one tell me is this the property of the scheme? Also where I can find materials regarding how to implement boundary conditions exactly in staggered grid? thank you,

Central difference schemes do not have inbuilt dissipation and hence when you keep refining the grid without adding stability,oscillations can be produced.This was the reason your code worked fine with increased numerical viscosity.You might want to look into the book of patankar ( Numerical heat tranfer and fluid flow) for more information on boundary condition implementation on staggered grid.For stability analysis of numerical schemes any finite difference or CFD books should provide you the information.

hi harish,

thanks for your reply.. But i cant understand what do you exactly mean by "when you keep refining the grid without adding stability,oscillations can be produced." I read, once we refine the grid, we should get more accurate solution. Can you give me some more explanations about your point?

Have a look into any CFD book for some discussion about dissipation and dispersion.It might help you.

http://www.cscamm.umd.edu/centpack/publications/#c4

thank you very much harish.. i think it will help me to make my code perfect...

hi all,

Now, I have observed that my final solution changes with respect to the under-relaxation factor used.. Also it converges only for very low under-relaxation values (nearly 0.1).. can any one explain me how to handle that factor properly in CFD?