This work details the development and validation of an unsteady
unstructured high order ( 3) h/p Discontinuous Galerkin (DG) -
Fourier solver for the incompressible Navier-Stokes equations on
static and rotating sliding meshes in 3D. This general purpose
solver is used to provide insight into cross-flow (wind or tidal)
turbine physical phenomena. To account for the relative mesh
motion, the system of equations is written in arbitrary
Lagrangian-Eulerian form and a non-conformal DG formulation is used
for spatial discretisation. The DG method, together with a novel
sliding mesh technique, allows direct linking of rotating and
static meshes through the numerical fluxes. This technique shows
spectral accuracy and no degradation of temporal convergence rates
if rotational motion is applied to a region of the mesh. To
simulate 3D flows, the solver is parallelised and extended using
Fourier series, which enables DNS and turbulent LES simulations.
Two LES methodologies are proposed. The thesis includes solutions
for: Stokes flows, the Taylor vortex problem, flows around square
and circular cylinders, flows around static and rotating NACA foils
and rotating cross-flow turbines flows."
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