A surface capturing method is developed for the computation of steady water–air flow with gravity. Fluxes are based on artificial compressibility and the method is solved with a multigrid technique and line Gauss–Seidel smoother. A test on a channel flow with a bottom bump shows the accuracy of the method and the efficiency of the multigrid solver.

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Elsevier
Journal of Computational and Applied Mathematics
Development of a State-of-the Art Surface-Capturing Method for Two-Fluid Flow
Scientific Computing

Wackers, J., & Koren, B. (2008). A surface capturing method for the efficient computation of steady water waves. Journal of Computational and Applied Mathematics, 215, 618–625.