A pressure-correction and bound-preserving discretization of the phase-field method for variable density two-phase flows. (English) Zbl 07524769
Summary: In this paper, we present an efficient numerical algorithm for solving the time-dependent Cahn-Hilliard-Navier-Stokes equations that model the flow of two phases with different densities. The pressure-correction step in the projection method consists of a Poisson problem with a modified right-hand side. Spatial discretization is based on discontinuous Galerkin methods with piecewise linear or piecewise quadratic polynomials. One important contribution of this work is the formulation of flux and slope limiting techniques that successfully eliminate the bulk shift, overshoot and undershoot in the order parameter. The bound-preserving property of the discrete order parameter is proved. Several numerical results demonstrate that the proposed numerical algorithm is effective and robust for modeling two-component immiscible flows in porous structures and digital rocks.
MSC:
| 76Mxx | Basic methods in fluid mechanics |
| 76Dxx | Incompressible viscous fluids |
| 65Mxx | Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems |
Keywords:
phase-field; pressure-correction projection; discontinuous Galerkin; flux limiters; slope limiters; digital rockReferences:
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