An efficient Navier-Stokes based numerical wave tank using fast Poisson solvers and the immersed boundary method

Abstract

An efficient numerical model for wave induced flows and their interaction with impermeable coastal structures, is presented. Using recent developments in the field of two-fluid (water/air) Navier-Stokes (NS) simulations, an efficient numerical wave tank (NWT) was developed which combines the Immersed Boundary (IB) method and Fast Direct Solvers (FDS). Conventional NS-based NWTs require significant computational resources which prevents their use in discretisation demanding cases or extensive parametric studies. The computational efficiency of the new NWT was achieved by replacing the conventional variable-coefficient Poisson equation with a constant-coefficient one which is solved with a FDS. Results of the accuracy, limitations, and computational performance of the NWT are presented and discussed based on several validation tests: (1) propagation of a 2nd-order Stokes wave, (2) formation of a standing wave, (3) spilling breaking over a mild slope bed, (4) three-dimensional (3D) interaction of a solitary wave with a vertical abutment, and (5) diffraction of a solitary wave by a single-row pile breakwater. The computational performance of the new NWT was demonstrated for problems with 1–280 million grid nodes. The overall speed-up of the new NWT increases with the problem size, and it is estimated to be about 30 for large 3D problems.