Moving Gresho Test

The moving Gresho vortex test is identical to the Gresho test describd in the previous post, except that the fluid is given a constant velocity boost in the x-direction. Here, I apply a velocity boost of \(v_x = 1.0\) and show the results at \(t = 3.0\), after the vortex has moved across the domain three times. I’m using periodic boundaries and a \(40\times40\) cell grid.

L1 error

The L1 errors at \(t = 3.0\) are 0.9% for density and 167% for vorticity. I’m not sure why the vorticity errors are so high in comparison to the ppm results in Liska & Wendroff, but I think it may have to do with the accuracy of my vorticity calculation. Looking at the initial conditions (shown in the previous post), the vorticity is already off from the exact solution by a lot. Given that the density errors are comparable to the results in LW03, I’d say this test looks about as good (bad) as I’d expect.