Numerical methods for multi scale hyperbolic problems, with application to multi-fluid and sedimentation

In this project we consider the development of a semi-implicit finite volume scheme for the numerical solution of multi scale hyperbolic systems. We consider two model problems: multi-fluid compressible Euler equations [1] and shallow water equations with standard bathymetry [2]. In both cases the equations are discretized on a non-staggered grid, adopting a method which is a generalization of the one proposed in [3]. Second order in space is obtained by WENO reconstruction for all the upwind derivatives and classical three point central scheme for the rest. Second order in time is achieved through an implicit-explicit Runge-Kutta scheme [4].