A Three-dimensional Multi-species Flow Solver for the Euler Equations Combined with a Stiffened Gas Equation of State

Abstract

Although numerical simulation in fluid mechanics is undergoing a significant development due to the dazzling evolution of computing means, complex physical phenomena, such as multidimensional viscous effects in turbomachinery and cavitation, remain mysterious and attract the curiosity of several researchers. Highresolution shock captures are often obtained by the WENO family of schemes, except that in problems that depend on discontinuities and shocks, an appearance of numerical oscillations weakens its ability to provide adequate captures. The use of the characteristic construction methods prevents this type of oscillation. The present paper contributes to the numerical resolution of multi-species flows of viscous, compressible, or incompressible fluids with shocks and discontinuities. The proposed numerical model can handle various configurations with a unique method based on a conservative and consistent threedimensional finite volume scheme with an aligned mesh. The system of equations is a set of Euler equations coupled with a two-parameters generalized state equation of state in three-dimensional Cartesian coordinates. This system is solved using a Roe type approximate Riemann solver, and second-order precision is obtained using limiters. The obtained numerical results maintain a nonoscillatory flow near the discontinuities, which makes the method satisfactory and shows its accuracy and robustness in different cases.