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| Remark:A total variation diminishing (TVD) scheme with a wave by wave characteristic limiting process is applied to the test problem in a mach 3 wind tunnel with a step (refer to the Woodward and Colella's 1984 paper). The problem begins with uniform Mach 3 flow in a wind tunnel containing a step. The wind tunnel is 1 length unit width and 3 length units along. The step is 0.2 length units high and is located 0.6 length units from the left-hand end of the tunnel. At the left is a flow-in boundary condition, and at the right all gradients are assumed to vanish. Along the walls of the tunnel reflecting boundary conditions are applied. Initially the wind tunnel is filled with a gamma-law gas, with gamma=1.4, which everywhere has density 1.4, pressure 1.0, and velocity 3.0. The corner of the step is the center of a rarefaction fan and is a singular point of the flow. However, in our experiments, no special boundary condition is applied there. Shown above are the adaptively refined grids at a time close to 4.0 and the isocontours of density. Click on the image, you may see a dynamic animation. |