Application of a High Order Finite Volume Scheme on Unstructured Grids to Fluid Dynamics and Aerothermochemistry

Abstract

This paper presents a high order finite volume scheme built on a new k-exact reconstruction algorithm for general unstructured grids. The algorithm is capable of computing accurate polynomial approximations using data from adjacent cells only, overcoming a major obstacle to extend classical finite volume schemes beyond 2 nd order spatial accuracy. Moreover, it can easily be integrated in a cell or vertex centered finite volume method that uses the cell averages as the only unknown per grid cell and physical quantity. It is therefore particularly suited to upgrade existing 2 nd order finite volume solvers to higher accuracy without huge efforts in software development. Three numerical test cases demonstrate the viability of the scheme in practical applications. This work was announced in [13, 14]