A Non Homogeneous Riemann Solver for Two-phase ShallowWater Flows

Abstract

The purpose of this research is to develop a simulation method for two-phase flows using shallow water equations. The hydraulics is modeled by the two-dimensional shallow water flows with variable horizontal density. The variation of density in the water flows can be attributed to the variation of thermal and salinity properties of the water. As an example of two-phase shallow water flows is the inclusion of the salty water from the sea into the fresh water of a river. Driving force of the phase separation and the mixing is the gradient of the density. For the numerical solution procedure we propose a non-homogeneous Riemann solver in the finite volume framework. The proposed method consists of a predictor stage for the discretization of gradient terms and a corrector stage for the treatment of source terms. The gradient fluxes are discretized using a modified Roe’s scheme using the sign of the Jacobian matrix in the coupled system. A well-balanced discretization is used for the treatment of source terms. The efficiency of the solver is evaluated by several test problems for two-phase shallow water flows. The numerical results demonstrate high resolution of the proposed non-homogeneous Riemann solver and confirm its capability to provide
accurate simulations for two-phase shallow water equations under flow regimes with strong shocks.