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Three-dimensional free-surface flow over arbitrary bottom topography

Published online by Cambridge University Press:  03 May 2018

Nicholas R. Buttle ,
Ravindra Pethiyagoda ,
Timothy J. Moroney  and
Scott W. McCue Open the ORCID record for Scott W. McCue [Opens in a new window]
Nicholas R. Buttle
Affiliation:
School of Mathematical Sciences, Queensland University of Technology, Brisbane QLD 4001, Australia
Ravindra Pethiyagoda
Affiliation:
School of Mathematical Sciences, Queensland University of Technology, Brisbane QLD 4001, Australia
Timothy J. Moroney
Affiliation:
School of Mathematical Sciences, Queensland University of Technology, Brisbane QLD 4001, Australia
Scott W. McCue*
Affiliation:
School of Mathematical Sciences, Queensland University of Technology, Brisbane QLD 4001, Australia
*
†Email address for correspondence: [email protected]
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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.

JFM classification

Waves/Free-surface Flows: Surface gravity waves Wakes/Jets: Wakes Waves/Free-surface Flows: Waves/Free-surface Flows
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 846 , 10 July 2018 , pp. 166 - 189
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Copyright
© 2018 Cambridge University Press 

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