convergence analysis for viscous problems
 

Hi,

I am trying to benchmark my higher order DG code for viscous problems. I devised a new method of representing the viscous flux at cell interface and am required to establish the order of accuracy of the proposed scheme.

I took the standard test case of isentropic vortex evolution problem as the initial setup and am trying to estimate the error as the difference between the solutions (at t=5) of the current grid and the refined grid. For example, if I have grids G1, G2, G3, the error for G1 would be |Q1-Q2| where Q is the solution on the grid. The error for G2 would be |Q2-Q3| and so on. Is this the right way to estimate the grid convergence if we do not know the analytical solution?
When I do the above test, I get acceptable grid convergence results. I am just wondering if it is the right way to do...

Shyam

That approach should give you the right order of convergence estimate (slope of log(err) v log(dx)), but won't give you an estimate of the constant multiplier out front (intercept of log(err) v log(dx)). To get that you would want to do something like: |Q1-Q4|, |Q2-Q4|, |Q3-Q4|, where the grid for Q4 is much finer than 1,2 and 3, but 1,2 and 3 are still in the asymptotic range. So you're basically treating Q4 as your analytic solution.

Not many people care about estimating the constant on the truncation error though.