Changes between Version 94 and Version 95 of u/erica/GudonovMethodEuler


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Timestamp:
05/08/13 15:02:44 (11 years ago)
Author:
Erica Kaminski
Comment:

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  • u/erica/GudonovMethodEuler

    v94 v95  
    181181The initial condition's for test 4 produce a left facing (originating from the left initial state) shock wave, traveling very slowly to the right, a right traveling contact, and a right traveling shock wave. This makes intuitive sense from the initial conditions:
    182182
    183 [[Image(test.png, 40%)]]
    184 [[Image(test4.png, 40%)]]
     183[[Image(test.png, 50%)]]
     184[[Image(test4.png, 50%)]]
    185185
    186186Now the EXACT solution at t=0.035 could be computed from the Exact Riemann Solver alone, and this would be by looping through the grid at different dx/dt = dx/0.035, to determine the relative position of this 'grid speed' to the shocks and contact waves generated at the boundary. If the grid speed is ahead of all shocks (far enough to the right, given all waves in this solution are traveling to the right), then the initial state is not yet disturbed, and so the EXACT solution there just is the initial condition there. The same holds true if the grid speed were far enough to the left, such that the entire system of generated waves has not interacted with the initial state. Now the tricky thing is to get the solution inside the wave structure, and honestly, it seems like something you'd ever only want to do with the help of a computer program, looping through tests and conditions to determine the new values of the disturbed initial condition. Here is the plot from Toro of the exact solution of Test 4 using the Exact Riemann Solver:
    187187
    188 [[Image(ExactTest4.png, 50%)]] 
     188[[Image(ExactTest4.png, 60%)]] 
    189189
    190190These plots make qualitative sense, based on the aforementioned concepts. Now... how does this change when we solve these initial conditions with the Godunov scheme?