Adaptive Grid Refinement

Burgers' Equation

In this example we consider a 2-D Riemann problem. Initially we have different constants in the four quadrants, as indicated in the figure to the right. At any positive time the solution consits of six shocks, two with speed 3/8, two with speed -1/8, and two stationary. Three shocks with different speed meet at two points.

Click on the link(s) below to see how the adaptive grid works on this problem. For each time step in the dimensional splitting algorithm, the grid with a contour plot imposed on top is shown at four different times in the algorithm. First we show the initial data for the x-sweep after preprocessing and the solution after front tracking and projection. Then we show the preprocessed data for the y-sweep and the projected solution after the sweep.

START the slide show.

[ Step 1 | Step 2 | Step 3 | Step 4 ]