Application of the simplified eigenstructure decomposition solver to the simulation of general multifield models

In this paper, we discuss an upwinding methodology for the numerical simulation of general multi-phase flows inspired by the generalized Roe type solver. Yet, while the Roe solver makes use of the entire eigenstructure of a system of balance equations, we present here a less complex alternative algorithm, called Simplified Eigenstructure DEcomposition Solver (SEDES), that uses only a partial eigenstructure information, based on the observation of the specific eigenvalue structure of the multi-phase flow model: two fast eigenvalues, always real and well separated from all the other remaining eigenvalues. The outcome is an easy to implement and relatively low CPU cost algorithm, which is accurate enough to respect the fine degree of physical modeling and able to deal with a higher degree of complexity in term of system size and physical models. This methodology has already been applied to two-fluid models and a number of numerical and physical benchmarks presented here illustrate that its generalization to multifield models is quite successful. Some comparisons between SEDES and Roe computational results shed light upon the issues of accuracy and robustness.

► A simplified eigenstructure decomposition solver for general multifield models. ► Solver construction based on the eigenvalue structure of multifield models. ► Easy to implement, accurate and relatively low CPU cost solver. ► A number of numerical and physical benchmarks assesses the solver. ► Comparisons with Roe solver illustrate solver's accuracy, robustness and efficiency.