Numerical simulation of hyperbolic two-phase flow models using a Roe-type solver

The application of the generalized Roe scheme to the numerical simulation of two-phase flow models requires a fast and robust computation of the absolute value of the system matrix. In several models such as the two-fluid model or a general multifield model, this matrix has a non-trivial eigenstructure and the eigendecomposition is often ill conditioned. We give a general algorithm avoiding the diagonalization process. It is based on an iterative approach, but turns out to be an exact computation when the eigenvalues are real. The knowledge of the characteristic polynomial gives us an easy access to the eigenvalues but however, the iterative scheme can be used with only estimates of the eigenvalues, using for example Gershgorin's disk localization. We finally show some numerical results of two-fluid model simulations involving interfacial pressure and a virtual mass force model