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Analysis of a regularized model for the isothermal two-component mixture with the diffuse interface. (English) Zbl 1422.65145
Summary: A regularized system of equations describing a flow of isothermal two-component mixture with diffuse interface is studied. The equation of energy balance and its corollary, i.e., the law of non-increasing of the total energy are derived under general assumptions on the Helmholtz free energy of the mixture. Necessary and sufficient conditions for linearized stability of constant solutions are obtained (in particular case). A difference approximation of the problem is constructed in the two-dimensional periodic case on a nonuniform rectangular grid. The results of numerical experiments demonstrate a qualitative well-posedness of the problem and the applicability of the criterion of linearized stabilization in the original nonlinear formulation.

MSC:
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
35Q35 PDEs in connection with fluid mechanics
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