  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 numerical
analysis highlights that a single top layer of quadrilaterals elements resolves
temporal instabilities in the numerical MEL scheme that are known to be
associated with mesh topology containing asymmetric element orderings. The
'surface variable only' free surface formulation based on introducing a
particle-following (Lagrangian) reference frame contains quartic nonlinear
terms that require proper treatment by numerical discretisation due to the
possibility of strong aliasing effects. We demonstrate how to stabilise this
nonlinear MEL scheme using an efficient combination of (i) global L2 projection
without quadrature errors, (ii) mild nonlinear spectral filtering and (iii)
re-meshing techniques. Numerical experiments revisiting known benchmarks are
presented, and highlights that modelling using a high-order spectral element
method provides excellent accuracy in prediction of nonlinear and dispersive
wave propagation, and of nonlinear wave-induced loads on fixed submerged and
surface-piercing bodies.
