Abstract
We consider the regularized 3D Navier-Stokes-Cahn-Hilliard equations describing isothermal flows of viscous compressible two-component fluids with interphase effects. We construct for them a new energy dissipative finite-difference discretization in space, i.e., with the non-increasing total energy in time. This property is preserved in the absence of a regularization. In addition, the discretization is well-balanced for equilibrium flows and the potential body force. The sought total density, mixture velocity and concentration of one of the components are defined at nodes of one and the same grid. The results of computer simulation of several 2D test problems are presented. They demonstrate advantages of the constructed discretization including the absence of the so-called parasitic currents.
Highlights
Multiphase microflows involving significant interphase and capillary effects are often appear in nature and technology
We construct for them a new energy dissipative finite-difference discretization in space, i.e., with the non-increasing total energy in time
The results of computer simulation of several 2D test problems are presented. They demonstrate advantages of the constructed discretization including the absence of the so-called parasitic currents
Summary
Multiphase microflows involving significant interphase and capillary effects are often appear in nature and technology. This paper is devoted to the construction of a new energy-dissipative finitedifference spatial discretization for the 3D QHD-regularized viscous compressible isothermal NSCH system of equations taking into account the potential body force, in the spatially periodic statement. This construction is based, firstly, on the recent dissipative discretizations of regularized barotropic and full 3D gas dynamics systems of equations from [26, 27] and, secondly, on the representation in the potential form of a term associated to the capillary forces in the momentum equation to [15, 16, 17]. We give some negative numerical results in the case where the regularization is absent
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