A high-order accurate unconditionally stable bound-preserving numerical scheme for the Cahn-Hilliard-Navier-Stokes equations
Abstract
A high-order numerical method is developed for solving the Cahn-Hilliard-Navier-Stokes equations with the Flory-Huggins potential. The scheme is based on the Qk finite element with mass lumping on rectangular grids, the second-order convex splitting method, and the pressure correction method. The unique solvability, unconditional stability, and bound-preserving properties are rigorously established. The key to bound-preservation is the discrete L1 estimate of the singular potential. Ample numerical experiments are performed to validate the desired properties of the proposed numerical scheme.
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