A new numerical algorithm for two-phase flows drift-flux model with staggered grid in porous media
Résumé
FLICA4 is a 3D compressible code dedicated to reactor core analysis. It solves a compressible drift-flux model for two-phase flows in a porous medium [2]. To define convective fluxes, FLICA4 uses a specific finite volume numerical method based on an extension of the Roe's approximate Riemann colocated solver [3]. Nevertheless, analysis of this method shows that at low Mach number, it is necessary to apply modifications to the 2D or 3D geometries on a cartesian mesh otherwise this method does not converge to the right solution when the mach number goes to zero [4]. For this reason, we apply a so-called "pressure correction". Although this correction is necessary to reach the required precision, it may produces some checkerboard oscillations in space in the situations we are interested in, especially in the 1D case. Since these checkerboard oscillations are sometimes critical and may lead to unstable solutions in some cases, we investigate another numerical algorithm to solve this compressible drift-flux model in the low Mach regim. The aim of this work is to propose a new compressible scheme accurate and robust at low Mach number on staggered grid since checkerboard oscillations cannot exist on this type of discretisation [8]. The accuracy and robustness of this new scheme are verified in low Mach regime with test cases describing a simplified nuclear core "Boiling channel". The behavior of this scheme is also tested in the compressible regime with or without shock waves.
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