The plots below illustrate the difference between computations on a moving mesh (left) and a fixed grid (right), both with the same number of grid points. The partial differential differential equations being solved are the Euler equations of gasdynamics:
The plots of density, , clearly demonstrate that the moving mesh method resolves all three solution features more accurately using the same number of grid points. The moving mesh method clearly displays much better shock resolution, and the plot of the mesh trajectories (at bottom) indicates how mesh points smoothly cluster together as the discontinuity develops, and then follow along with the shock. The mesh contours at the bottom indicate how the mesh points track the shock and contact line.
Moving mesh solution (N=60) | Fixed mesh solution (N=60) |
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