We present an arbitrary-order spectral element method for general-purpose simulation of
non-overturning water waves, described by fully nonlinear potential theory. The method can
be viewed as a high-order extension of the classical finite element method proposed by Cai
et al.(1998)[5], although the numerical implementation differs greatly. Features of the
proposed spectral element method include: nodal Lagrange basis functions, a general
quadrature-free approach and gradient recovery using global L 2 projections. The quartic …

We present a new stabilised and efficient high-order nodal spectral element method based
on the Mixed Eulerian Lagrangian (MEL) method for general-purpose simulation of fully
nonlinear water waves and wave-body interactions. In this MEL formulation a standard
Laplace formulation is used to handle arbitrary body shapes using unstructured-possibly
hybrid-meshes consisting of high-order curvilinear iso-parametric quadrilateral/triangular
elements to represent the body surfaces and for the evolving free surface. Importantly, our …