Geodesic
A New Numerical algorithm for two-phase flows drift-flux model with staggered grid in porous media
Anouar Mekkas1 ; Anne Charmeau1 ; Sami Kouraichi2
1 CEA/DEN/DM2S/STMF F-91191, Gif-sur-Yvette, France
2 Université Paris 13, 99 Avenue Jean Baptiste Clément, 93430 Villetaneuse, France
ESAIM. Proceedings, Tome 58 (2017), pp. 58-77.

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FLICA4 is a 3D compressible code dedicated to reactor core analysis. FLICA4 solves for two-phase flows in porous media using a compressible drift-flux model [2]. To derive convective fluxes, FLICA4 uses a specific finite volume numerical method based on an extension of the Roe’s approximate Riemann colocated solver [3]. The method is developped to solve 1D flows. It requires adjustments to solve for 2D or 3D flows, at low Mach number, on a cartesian mesh. As Mach number goes to zero, in some extreme 2D or 3D cases, the native method does converge but the solution is not consistent with the analytical or experimental solution [4]. A so-called “pressure correction“ is added to the initial solver to derive an accurate solution. However, this extra term produces checkerboard oscillations in space for most applications of interest, even when solving for 1D flows. These checkerboard oscillations are sometimes critical and may lead to unstable solutions or divergence of the solver. The paper presents the analysis of an alternative numerical algorithm to solve for compressible drift-flux model in the low Mach regime. The current study aims at investigating a new compressible scheme that is both accurate and robust at low Mach number on staggered grids. The actual behavior of the new scheme is tested against simplified nuclear core ”boiling channel” study cases in the low Mach regime. The tests are extended to compressible regime for flows exhibiting both shock waves and no shock waves. The paper shows that the alternative numerical algorithm leads to numerical solutions that are very close to analytical solutions. Moreover, no more checkboard oscillations are generated. Therefore, the algorithm is a real improvement to FLICA4 current numerical method.
DOI : 10.1051/proc/201758058

Anouar Mekkas 1 ; Anne Charmeau 1 ; Sami Kouraichi 2

1 CEA/DEN/DM2S/STMF F-91191, Gif-sur-Yvette, France
2 Université Paris 13, 99 Avenue Jean Baptiste Clément, 93430 Villetaneuse, France 
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     title = {A {New} {Numerical} algorithm for two-phase flows drift-flux model with staggered grid in porous media},
     journal = {ESAIM. Proceedings},
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Anouar Mekkas; Anne Charmeau; Sami Kouraichi. A New Numerical algorithm for two-phase flows drift-flux model with staggered grid in porous media. ESAIM. Proceedings, Tome 58 (2017), pp. 58-77. doi : 10.1051/proc/201758058. http://geodesic.mathdoc.fr/articles/10.1051/proc/201758058/

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