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We present a new stabilised and efficient high-order nodal spectral elementmethod based on the Mixed Eulerian Lagrangian (MEL) method for general-purposesimulation of fully nonlinear water waves and wave-body interactions. In thisMEL formulation a standard Laplace formulation is used to handle arbitrary bodyshapes using unstructured - possibly hybrid - meshes consisting of high-ordercurvilinear iso-parametric quadrilateral/triangular elements to represent thebody surfaces and for the evolving free surface. Importantly, our numericalanalysis highlights that a single top layer of quadrilaterals elements resolvestemporal instabilities in the numerical MEL scheme that are known to beassociated with mesh topology containing asymmetric element orderings. The'surface variable only' free surface formulation based on introducing aparticle-following (Lagrangian) reference frame contains quartic nonlinearterms that require proper treatment by numerical discretisation due to thepossibility of strong aliasing effects. We demonstrate how to stabilise thisnonlinear MEL scheme using an efficient combination of (i) global L2 projectionwithout quadrature errors, (ii) mild nonlinear spectral filtering and (iii)re-meshing techniques. Numerical experiments revisiting known benchmarks arepresented, and highlights that modelling using a high-order spectral elementmethod provides excellent accuracy in prediction of nonlinear and dispersivewave propagation, and of nonlinear wave-induced loads on fixed submerged andsurface-piercing bodies.

A Stabilised Nodal Spectral Element Method for Fully Nonlinear Water Waves, Part 2: Wave-body interaction