A mass–momentum consistent coupling for mesh-adaptive two-phase flow simulations. (15th February 2023)

• Record Type: Journal Article
• Authors: Kuhn, Michael B.; Deskos, Georgios; Sprague, Michael A.
• Is Part Of: Computers & fluids. Volume 252(2023)
• Publication Date: 2023-02-15
• Subjects: Two-phase flows -- Mass–momentum consistency -- Volume-of-fluid -- Ocean waves -- Adaptive mesh refinement; Fluid dynamics -- Data processing -- Periodicals; 532.050285
• DOI: 10.1016/j.compfluid.2022.105770
• Languages: English
• ISSNs: 0045-7930

Abstract

Abstract: We present a novel mass–momentum consistent coupling between a geometric volume-of-fluid scheme and an incompressible flow solver with differing directional-splitting approaches. The advection of the volume fraction is performed using a direction-split algorithm, whereas the momentum advection algorithm uses a traditional unsplit, fractional-step approach. Both algorithms employ finite-volume discretizations based on Cartesian meshes. In solving the mass–momentum consistency problem, momentum fluxes at the cell faces are weighted by the density fluxes based on the already advected volume fraction. The success of our approach lies on introducing a Favre-averaged velocity interpolation at the liquid/gas interface along with a minmod slope limiter. Mesh-convergence studies show that when the minmod slope limiter is used, the two-phase solver retains an accuracy between first and second order, but when a purely upwind scheme is considered, its accuracy drops to first order. Finally, after considering several validation problems, the solver is shown to agree well with reference numerical and experimental data while retaining its robustness and efficiency. Highlights: Numerical technique couples split volume fraction and unsplit momentum solves. Mass–momentum consistency enables stability for simulating free-surface flows. Accuracy approaches second-order in verification tests. Analysis of upwind and minmod interpolation schemes in validation.