Application of Non-Reflective Boundary Conditions in Three-Dimensional Numerical Simulations of Free-Surface Flow Problems

Abstract

This paper considers the issue of using non-reflective boundaries for surface wave simulations within the framework of three-dimensional Navier–Stokes equations. We distinguish a wave damping approach among the known implementations of non-reflective boundary conditions in surface wave simulations. The approach employs a sponge boundary layer to dampen incident waves. In this paper, we describe implementations of this approach on unstructured meshes. We also present the calibration of free parameters, the values of which control wave damping efficiency and the amplitude of reflected waves. Comparison of the results obtained at different types of distribution for the free parameter was conducted. The implemented wave damping approach was tested by simulating a solitary wave propagating in a water tank. We demonstrate the use of damping non-reflective boundary conditions for the case of a wave traveling across the surface of a real body of water near Sakhalin Island while considering its bathymetry.

Keywords

• tsunami
• numerical simulation
• Navier–Stokes equations
• VOF method
• wave damping
• LOGOS software package