An efficient method for the computation of steady water-air flow with gravity is presented. The method is designed for fast solution using multigrid, combined with a line Gauss-Seidel smoother. A capturing model is used for the water surface, with fluxes based on artificial compressibility. A test on a channel flow with a bottom bump shows the accuracy of the method and the efficiency of the multigrid solver.

steady water waves, surface capturing, multigrid, artificial compressibility, Osher flux function"
Multigrid methods; domain decomposition (msc 65N55), Navier-Stokes equations (msc 76D05), Waves (msc 76D33)
Life Sciences (theme 5), Energy (theme 4)
Modelling, Analysis and Simulation [MAS]
Scientific Computing

Wackers, J, & Koren, B. (2007). A multigrid method for the computation of steady water waves. Modelling, Analysis and Simulation [MAS]. CWI.