Version 18 (modified by 12 years ago) ( diff ) | ,
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The Godunov Method for Euler Equations, using EXACT Riemann Solver
Big Picture
- Define a piece-wise function of initial data
- Solve the IVP for the original conservation law, but with modified (discretized) initial data to get the solution for the next time level
- This produces local Riemann Problems (RPs), centered on intercell boundaries.
- Solve these local RP's, and use solution to compute fluxes
The method
In conservative form, the Godunov method is written:
where
is the numerical flux, which = the physical flux evaluated along the intercell boundary using the exact solution to the local Riemann Problem (LRP).
The time-step, is constrained by the CFL condition, which uses the max wave speed on the grid. The constraint used in the God. code here allows any given wave on the grid to travel a full delta_x in a time-step. In allowing this, we achieve a more efficient time-marching scheme, but with the assumption that wave interactions do not lead to wave accelerations.
The code
Here is an html version of the main program, with encompassing module, and problem.data file.
Debugging
Results
Attachments (14)
- GodEulRho.png (19.0 KB ) - added by 12 years ago.
- GodEulP.png (21.1 KB ) - added by 12 years ago.
- GodEulU.png (22.3 KB ) - added by 12 years ago.
- God.2.png (50.2 KB ) - added by 12 years ago.
- God.png (50.2 KB ) - added by 12 years ago.
- LoopSR.png (44.1 KB ) - added by 12 years ago.
- program_out.png (28.7 KB ) - added by 12 years ago.
- God_density_init.png (12.8 KB ) - added by 12 years ago.
- God_density.png (21.5 KB ) - added by 12 years ago.
- GodDebug.png (72.1 KB ) - added by 12 years ago.
- test.png (5.8 KB ) - added by 12 years ago.
- test4.png (8.7 KB ) - added by 12 years ago.
- ExactTest4.png (29.1 KB ) - added by 12 years ago.
- GodTest4.png (37.9 KB ) - added by 12 years ago.
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