Benchmarking of Navier-Stokes codes for free surface simulations by means of a solitary wave

摘要

The paper presents a benchmark of four freely available solvers for Navier-Stokes equations: Gerris, OpenFOAM, Thetis and Truchas. These models are selected because they have been reported to deal successfully with ocean-ographic and coastal engineering applications. The benchmark includes two free surface problems: propagation of a solitary wave and runup of a solitary wave on a plane beach. The fluids are inviscid, which allows a detailed study of energy conservation and comparison of the results with a reference solution given by a boundary integral solver. The Navier-Stokes solvers use the finite volume discretization and free surface capturing techniques based on the volume-of-fluid (VOF) method. In the first benchmark test, we investigate the influence of numerical dissipation and other spurious effects on the energy balance of the wave. In the second problem, we focus on the runup heights and compare them with the reference solution. The beach in the runup problem is represented with a solid body immersed in the Cartesian mesh. The solid boundaries are described with a VOF type approach or a staircase representation, depending on the features of the solver. In addition to the immersed boundary description a couple of body fitted meshes are tested for the runup case.