Run-up simulation of impulse-generated solitary waves

Abstract

A numerical method is presented to accurately simulate paddle-generated impulse waves. An order-one implicit splitting scheme allows advection and diffusion phenomena to be decoupled. Advection is solved using a semi-Lagrangian scheme implemented on a dynamic adaptive octree. This method enables the use of Courant numbers larger than one while the octree is refined at the liquid–air interface. Diffusion is solved on a fixed, unstructured finite-element tetrahedral mesh. Interpolation between octree and finite elements is discussed. Numerical results pertaining to paddle-generated waves in a tilted cavity are successfully compared with experimental data.