alexpapados / 2-D-Compressible-Euler-Equations-FVM

C++ implementation of the finite volume method with flux-limiting to solve 2-D compressible Euler Equations (Liska, 2003)

2-D Compressible Euler Equations -- Hydrodynamic Shock-Tube Problem (C++ Implementation)

Author: Alexandros Papados

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This repository is dedicated to provide users of interests with the ability to solve 2-D hydrodynamic shock-tube problems using the finite volume method with flux limiting in C++. The 2-D problem of interest stems from (Liska, 2003). The paper may be found below.

This code makes use of RK-2 to integration in time, the HLLE flux solver, and the monotonized central flux limiter. As of now, the initial state is hardcoded, but may be easily changed to solve various shock-tube problems. The solution to this problem is shown in the figure below.

Initial State of density and pressure (top) Final State of density and pressure (bottom)

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In-progress

• Implement various flux solvers and limiters
• Generalized initial condition function
• MPI implementation
• Write-up discussing schemes and problem

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References

Paper: https://www.researchgate.net/publication/228781823_Comparison_of_Several_Difference_Schemes_on_1D_and_2D_Test_Problems_for_the_Euler_Equations

Code: https://github.com/wme7/Euler