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Numerical resolution of a potential diphasic low Mach number system. (English) Zbl 1163.76035
The diphasic low Mach number (DLMN) system models non-stationary deformations of an interface separating two immiscible fluids induced by large temperature differences at low Mach numbers. As the divergence of the velocity field is nonzero because of large temperature differences that induce compressibility effects, the DLMN system is a non-homogeneous diphasic incompressible Navier-Stokes system.
The author proposes a two-dimensional algorithm for the numerical discretization of the DLMN system in order to capture the interface separating two immiscible fluids on a fixed Cartesian mesh. Numerical results demonstrate that 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. This is used to conclude that the proposed algorithm is accurate and stable.

MSC:
76M20 Finite difference methods applied to problems in fluid mechanics
76T99 Multiphase and multicomponent flows
35Q35 PDEs in connection with fluid mechanics
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
80M20 Finite difference methods applied to problems in thermodynamics and heat transfer
Software:
HE-E1GODF
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