Abstract:
Higher resolution and reliability are the desiderata for Computational Fluid Dynamics
and main drivers for the development, implementation and validation of highorder
accurate methods. Complex fluid dynamic phenomena such as shock-wave
boundary-layer interactions, turbulent separated flows and fluid problems involving
multiple scales are adequately resolved with high-order schemes. The spatial representation
of the flow field by an unstructured mesh provides flexibility, automation,
fast and effortless grid generation and exceptional load balance on multiple processor
computers. This plethora of advantages is mirrored by the unprecedented popularity
of unstructured-based schemes.
The objective of this PhD project is the implementation of two high-order schemes
for the compressible Navier-Stokes equations in the context of the finite volume “kexact”
framework: the MUSCL-TVD and WENO. The schemes are formulated in
two and three space dimensions for mixed-element unstructured meshes; in addition,
the Spalart-Allmaras turbulence model is implemented into the developed numerical
framework. A wide range of applications are considered spanning from low-speed
flows (M = 0.08) to supersonic conditions (M = 5.0); inviscid and viscous simulations
in a broad spectrum of Reynolds numbers ranging from Re = 500 up to Re = 37×106.
The applications include: the Taylor-Green vortex, the ONERA-M6 wing, flat plate,
the NACA-0012 and the MD 30P-30N aerofoils, and a shock-wave boundary-layer
interaction.
For the examined cases, WENO schemes demonstrate superior accuracy, numerical
dissipation and non-oscillatory behaviour over the MUSCL-TVD. High-order schemes
inherit low numerical dissipation properties while turbulence models induce dissipation,
this disequilibrium has adverse effects on the stability, convergence and accuracy
of the simulation; therefore, turbulence model re-calibration would be required in order
to accommodate high-order discretisation methods.
