Changes between Version 96 and Version 97 of u/erica/GudonovMethodEuler
 Timestamp:
 05/08/13 15:16:53 (12 years ago)
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u/erica/GudonovMethodEuler
v96 v97 196 196 [[Image(GodTest4.png, 50%)]] 197 197 198 It is interesting to see the Godunov method performs quite well for the pressure and velocity, but falls short with density (and hence internal energy, which is a function of density). As I have shown above, we see the development of the structure that is trying to mimic the discontinuous density in the star region of the exact solution. By solving the Riemann problem with the Godunov method over successive time steps, we have smoothed out this region in our discretization of the problem. This must happen when we are inside of the star region, and there is a discontinuity that occurs in a fluid variable. I can imagine this smoothing happening only within the (global) star region , as outside of that region, the waves have not yet penetrated the surrounding medium. Given the only variable with the potential of not being continuous in this region is density, I imagine the only smoothing we see of sharp peaks in the solution is with density, and any quantities that depend on density. This then supports why we see close agreement with pressure and velocity between methods. 199 198 200 === Why Use One Method Over the Other === 199 201 200 201 How does the God solver modify the solution from the Exact Riemann solver? Why would you want to use the God scheme over an exact riemann solver? 202 You can imagine a situation with a much more complicated initial condition than just a flat left and right state separated by a discontintuity, but rather a series of discontinuites. For a system such as this, it seems to be straightforward to evolve the initial condition over time. In contrast, an exact solution for such a system seems nontrivial. 202 203 203 204 == Outstanding Questions == 204 205 205 206 1. Do we see an effect of the waves to spread away from the discontinuity? Yes! 206 2. What waves are generated from the type of discontinuity  consider what the exact riemann solver alone would do207 2. What is the effect of choosing a gamma=1.4? How would a different gamma affect the outcome of these results?