4.7 Article

Dissipative spatial discretization of a phase field model of multiphase isothermal fluid flow

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On a New Spatial Discretization for a Regularized 3D Compressible Isothermal Navier-Stokes-Cahn-Hilliard System of Equations with Boundary Conditions

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Summary: A new spatial finite difference discretization for a regularized 3D Navier-Stokes-Cahn-Hilliard system of equations is presented, which eliminates spurious currents completely and ensures mass conservation and well-balanced equilibrium solutions. The use of a special logarithmic form of the Helmholtz free energy allows for concentration within a physically meaningful range and enables the speed of sound to vary with concentration, leading to different equilibrium mass densities. The results of numerical 3D simulations, including those with gravitational-type force, and the positive role of the relaxation parameter are also discussed.

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