We present a high-order nodal spectral element method for the two-dimensional simulationof nonlinearwaterwaves. The model is based on themixed Eulerian–Lagrangian(MEL) method. Wave interaction with fixed truncated structures is handled usingunstructured meshes consisting of high-order iso-parametric quadrilateral/triangularelements to represent the body surfaces as well as the free surface elevation. A numericaleigenvalue analysis highlights that using a thin top layer of quadrilateral elementscircumvents the general instability problem associated with the use of asymmetricmesh topology.We demonstrate howto obtain a robustMELscheme for highly nonlinearwavesusing an efficient combination of (i) global L2 projectionwithout quadratureerrors, (ii) mild modal filtering and (iii) a combination of local and global re-meshingtechniques. Numerical experiments for strongly nonlinear waves are presented. Theexperiments demonstrate that the spectral element model provides excellent accuracyin prediction of nonlinear and dispersive wave propagation. The model is also shownto accurately capture the interaction between solitary waves and fixed submerged andsurface-piercing bodies. The wave motion and the wave-induced loads compare wellto experimental and computational results from the literature.