Exact Solvers
Godunov is credited with introducing the first exact Riemann solver for the Euler equations, by extending the previous CIR (Courant-Isaacson-Reeves) method to non-linear systems of hyperbolic conservation laws. Modern solvers are able to simulate relativistic effects and magnetic fields.
For the hydrodynamic case latest research results showed the possibility to avoid the iterations to calculate the exact solution for the Euler equations.
Read more about this topic: Riemann Solver
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