Numerical resolution of a potential diphasic low Mach number system

We propose a bidimensional algorithm for the numerical discretization of a diphasic low Mach number (DLMN) system in the case of a potential approximation, the extension to the tridimensional geometry being natural. In this algorithm, we capture the interface separating two immiscible fluids on a fixed cartesian mesh with an interface capturing algorithm. This algorithm solves a transport equation applied to an Heaviside function with a non-diffusive scheme i.e. with a scheme diffusing on a number of cells which is independent of the time integration. To take into account the artificial mixture area produced by this numerical diffusion, we have previously extended the DLMN system to the case of a mixture. Numerical results show that the algorithm is accurate and stable since the thickness of the artificial mixture area is always bounded by a constant which is of the order of the cell size, even in the case of important deformations of the interface, and since the numerical solution converges toward a good thermodynamic equilibrium with a decreasing of the entropy.