The successful application of Computational Aeroacoustics (CAA) requires high accuracy
numerical schemes with good dissipation and dispersion characteristics. Unstructured
meshes have a greater geometrical flexibility than existing high order structured
mesh methods. This work investigates the suitability of unstructured mesh techniques
by computing a two-dimensionallinearised Euler problem with various discretisation
schemes and different mesh types. The goal of the present work is the development of
an unstructured numerical method with the high accuracy, low dissipation and low dispersion
required to be an effective tool in the study of aeroacoustics. The suitability of
the unstructured method is investigated using aeroacoustic test cases taken from CAA
Benchmark Workshop proceedings. Comparisons are made with exact solutions and a
high order structured method.
The higher order structured method was based upon a standard central differencing
spatial discretisation. For the unstructured method a vertex-based data structure is
employed. A median-dual control volume is used for the finite volume approximation
with the option of using a Green-Gauss gradient approximation technique or a Least
Squares approximation. The temporal discretisation used for both the structured and
unstructured numerical methods is an explicit Runge-Kutta method with local timestepping.
For the unstructured method, the gradient approximation technique is used to compute
gradients at each vertex, these are then used to reconstruct the fluxes at the control
volume faces. The unstructured mesh types used to evaluate the numerical method include
semi-structured and purely unstructured triangular meshes. The semi-structured
meshes were created directly from the associated structured mesh. The purely unstructured
meshes were created using a commercial paving algorithm. The Least Squares
method has the potential to allow high order reconstruction. Results show that a
Weighted Least gradient approximation gives better solutions than unweighted and
Green-Gauss gradient computation. The solutions are of acceptable accuracy on these
problems with the absolute error of the unstructured method approaching that of a high
order structured solution on an equivalent mesh for specific aeroacoustic scenarios.
A Doctoral Thesis. Submitted in partial fulfilment of the requirements for the award of Doctor of Philosophy of Loughborough University.