Comparison of high-order methods on unstructured grids

A high-order Discontinuous Galerkin (DG) method is formulated and implemented on the Cranfield University’s 3D unstructured Finite Volume Method (FVM) code (UCNS3D), for both linear and non-linear hyperbolic conservation laws and for test-cases which exhibit both smooth and discontinuous solutions. As both DG and FVM are developed on the same solver platform, this enables the use of any procedures which are common to both the methods, thus, ensuring the closest possible compari-son. The initial part of the thesis details the basic concepts and derivation of the discon-tinuous Galerkin method in the 1D space for the advection equation, which is then extended to the 3D space for a hyperbolic system. Prior to comparing the FVM and DG methods, the DG method implementation is verified. The verification is a combination of a theoretical and numerical approach which endeavours to minimize any potential programming errors. Following the verification of the DG method, the FVM and DG methods are compared for numerous flows: the linear advection equation and Euler equations, sufficiently smooth testcases, and testcases which require a limiter to suppress Gibb’s oscillations.