What happens when you make your grid much finer than is required. Does it spoil the solution?

Shuo

your excercise?

No, just that I am using a TVD code and it gives problems when I make the grid very fine. Not too sure why this is the case.

ok (it was a joke)

theoritically, refinement of grid decrease truncation error; assume all of our approximation like a taylor approximation and so truncation error is porportional to O(h)^n+1, n is order of approximation. in the other hand, decreasing grid size increase round of error (intrinsic error related to computer arithmetic), however in practic we do not usually refine so the later be a case, however it is easy to check.

if your method has an implicit phase, it may be source of problem. e.g., if you have an iterative solver by grid refinement required number of iteration to solve system of equation is naturally increased and so you may not reach to desired accuracy within adjusted maximum number of iterations, so you can increase this maximum bond and check results.

if you have a nonlinear solver (outer iteration) its convergence can be also mater

another source maybe due to memory leak (using un-dynamic arrays), if your code be fortran 77, surely it use priori defined arrays with known maximum bound, and so you may hit this maxium bound by refinement.

Increasing the number of cells decreases the discretization error, the rounding off error is more related to the number of mathematical operations executed (number of iterations) so if refining the mesh reduces the number of iterations, you are in good shape, if not, well it is up to you. And remember, refining the mesh will increase the execution time per iteration, in case the time is important for you. Good Luck