Finding an Approximate Riemann Solver via Relaxation: Concept and Advantages

We first explain the general concept of relaxation models using the Jin-Xin model for scalar conservation laws. Then we consider the Suliciu model specifically for the homogeneous Euler equations. In a third step, using a two-speed relaxation model for the Euler equations with gravity as an example, we show how the construction of the relaxation system can endow the resulting method with useful properties. Finally, these properties are verified in numerical tests.