Orateur
Anouar Mekkas
(CEA Saclay, France)
Description
FLICA4 is a 3D compressible code specially devoted to reactor core analysis which solves a compressible drift-flux model for two-phase flows in a porous medium. To define convective fluxes, FLICA4 uses a specific finite volume numerical method based on an extension of the Roe’s approximate Riemann colocated solver. Nevertheless, an analysis of this type of method shows that in 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 tends to zero. 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, especially in the 1D case.
Since these checkerboard oscillations are sometimes critical and may lead to unstable resolutions or even divergence in some cases, we also investigate another numerical algorithm to solve this compressible drift-flux model in the low Mach regim. The key point is to develope a compressible solver on staggered grid since checkerboard oscillations cannot exist on this type of discretisation. The aim of this work is to present such a compressible scheme and to validate it in low Mach regime with test cases describing a simplified nuclear core.
The compressible solver on staggered grid that we develope follows the finite volume approach for all the balance equations. The time discretization of the equations is based on a semi-implicit scheme. As the equations are not linear, the solution at each time step is obtained by a Newton-Raphson iterative method. This method gives a linear system of equations for the increments of the principal variables. The chosen solution algorithm consists at first in eliminating the velocity increments as functions of the pressure incre- ments by rewriting the momentum equations. Substituting the velocity increments into the non-linear system gives a system involving only the pressure increments. The successive elimination of the scalar variables other than the pressure variable gives a linear system on the pressure. The resolution of this linear system will allow to determine the velocity and the other variables. We will present preliminary numerical experiments will be presented and compare them with analytic solutions.
