In this thesis, a high-order incompressible Navier-Stokes solver is developed in the
Python-based PyFR framework. The solver is based on the artificial compressibility
formulation with a Flux Reconstruction (FR) discretisation in space and explicit
dual time stepping in time. In order to reduce time to solution, explicit convergence
acceleration techniques are developed and implemented. These techniques include
polynomial multigrid, a novel locally adaptive pseudo-time stepping approach and
novel stability-optimised Runge-Kutta schemes.
Choices regarding the numerical methods and implementation are motivated as
follows. Firstly, high-order FR is selected as the spatial discretisation due to its low
dissipation and ability to work with unstructured meshes of complex geometries. Be-
ing discontinuous, it also allows the majority of computation to be performed locally.
Secondly, convergence acceleration techniques are restricted to explicit methods in
order to retain the spatial locality provided by FR, which allows efficient harnessing
of the massively parallel compute capability of modern hardware. Thirdly, the solver
is implemented in the PyFR framework with cross-platform support such that it can
run on modern heterogeneous systems via an MPI + X model, with X being CUDA,
OpenCL or OpenMP. As such, it is well-placed to remain relevant in an era of rapidly
evolving hardware architectures.
The new software constitutes the first high-order accurate cross-platform imple-
mentation of an incompressible Navier-Stokes solver via artificial compressibility. The
solver and the convergence acceleration techniques are validated for a range of turbu-
lent test cases. Furthermore, performance of the convergence acceleration techniques
is assessed with a 2D cylinder test case, showing speed-up factors of over 20 relative
to global RK4 pseudo-time stepping when all of the technologies are combined. Fi-
nally, a simulation of the DARPA SUBOFF submarine model is undertaken using the
solver and all convergence acceleration techniques. Excellent agreement with previ-
ous studies is obtained, demonstrating that the technology can be used to conduct
high-fidelity implicit Large Eddy Simulation of industrially relevant problems at scale
using hundreds of GPUs.