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Regular version of the site

Article

Analysis of a regularized model for the isothermal two-component mixture with the diffuse interface

Balashov V., Zlotnik Alexander, Savenkov E.

A study of a regularized quasi-hydrodynamic system of equations for the two-component isothermal mixture with the diffuse interface is accomplished. Under general assumptions on the Helmholtz free energy of the mixture, the energy balance equation with non-positive energy production and its corollary, the law of non-increasing total energy, are derived. The necessary and sufficient conditions for the linearized stability of constant solutions are derived (in a particular case).      A finite-difference approximation of the problem is constructed in the 2D periodic case for a non-uniform rectangular mesh. The results of numerical experiments are presented which demonstrate the qualitative correctness of the model and applicability of the linearized stability criterion in the original nonlinear statement.