Characterization of particle rebound phenomena in the erosion of turbomachinery

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/77337/1/AIAA-44864-924.pd

Extension of the Local Problem Error Estimate to the Finite Volume Discretisation

this paper, LPEE will be extended to allow its use in conjunction with the Finite Volume (FV) type of discretisation. The extension consists of three parts: an appropriate definition of a residual in the FV framework, a procedure for the calculation of self-equilibrating fluxes based on the conservative properties of the FV solution and a simplified solution method for the Local Problem. The paper also covers the extensions of the Local Problem Error Estimate to the convection-diffusion and the Navier-Stokes problem, following [2] and [3], respectively. The Local Problem Error Estimate is tested on three test cases with analytical solutions, where its performance is shown to be similar as in the case of the Finite Element discretisation

High Resolution NVD Differencing Scheme for Arbitrarily Unstructured Meshes

The issue of boundedness in the discretisation of the convection term of transport equations has been widely discussed. A large number of local adjustment practices has been proposed, including the well-known TVD and NVD families of differencing schemes. All of those use some sort of an "unboundedness indicator" in order to determine the parts of the domain where intervention in the discretisation practice is needed. These, however, all use the "far upwind" value for each face under consideration, which is not appropriate for unstructured meshes. This paper proposes a modification of the NVD criterion which localises it and thus makes it applicable irrespective of the mesh structure, thus facilitating the implementation of "standard" bounded differencing schemes on unstructured meshes. Based on this strategy, a new bounded version of Central Differencing constructed on the compact computational molecule is proposed and its performance is compared with other popular differencing schemes..