Three dimensional free-surface flow over arbitrary bottom topography
arXiv:1709.08803 · doi:10.1017/jfm.2018.254
Abstract
We consider steady nonlinear free surface flow past an arbitrary bottom topography in three dimensions, concentrating on the shape of the wave pattern that forms on the surface of the fluid. Assuming ideal fluid flow, the problem is formulated using a boundary integral method and discretised to produce a nonlinear system of algebraic equations. The Jacobian of this system is dense due to integrals being evaluated over the entire free surface. To overcome the computational difficulty and large memory requirements, a Jacobian-free Newton Krylov (JFNK) method is utilised. Using a block-banded approximation of the Jacobian from the linearised system as a preconditioner for the JFNK scheme, we find significant reductions in computational time and memory required for generating numerical solutions. These improvements also allow for a larger number of mesh points over the free surface and the bottom topography. We present a range of numerical solutions for both subcritical and supercritical regimes, and for a variety of bottom configurations. We discuss nonlinear features of the wave patterns as well as their relationship to ship wakes.
28 pages, published by Journal of Fluid Mechanics
References in corpus (8)
- What is the apparent angle of a Kelvin ship wave pattern?
- Ship waves on uniform shear current at finite depth: wave resistance and critical velocity
- Time-frequency analysis of ship wave patterns in shallow water: modelling and experiments
- Spectrograms of ship wakes: identifying linear and nonlinear wave signals
- Jacobian-free Newton-Krylov methods with GPU acceleration for computing nonlinear ship wave patterns
- Surface waves on arbitrary vertically-sheared currents
- Wake angle for surface gravity waves on a finite depth fluid
- Efficient computation of two-dimensional steady free-surface flows