The ability to predict the wave climate has a great impact on a wide range of sectors,
including coastal and offshore engineering, marine renewable energy and shipping.
The state of the art in wave prediction is called spectral wave modelling and is based
on a phase-averaged, spectral description of the sea-surface elevation. The governing
equation, called the action balance equation, is five-dimensional and describes the
generation, propagation and evolution of action density in geographic space, spectral
space and time. Due to the multidimensional nature of the equation the feasible
resolutions are restricted by the computational costs. The aim of this work is to
propose schemes which can increase the range of possible resolutions in spectral wave
modelling, with the use of adaptivity in space and angle. Thus, this work focuses
on the development of an unstructured, adaptive finite element spectral wave model
(Fluidity-SW).
A sub-grid scale model for the spatial discretisation is used, which retains the stability of discontinuous systems, with continuous degrees of freedom. Then, a new
framework for angular adaptivity is developed, with results in dynamic angular and
spatial anisotropy of the angular mesh. Finally a spatially h−adaptive scheme is implemented, which can dynamically treat the spatial gradients of the solution fields.
The resulting framework is thoroughly verified and validated in a wide range of test
cases and realistic scenarios, against analytical solutions, wave measurements and
the results obtained with the widely used SWAN model. Thus, the overall ability of
the code to simulate surface gravity wind-waves in fixed and adaptive spatial and
angular meshes is demonstrated.