Analysis and implementation of a high-order reconstruction algorithm for an unstructured finite volume flow solver

A high-order scheme is examined an implemented in an unstructured solver. The motivation for this researcher is driven by research goals to simulate field equations, particularly those of fluid dynamics, with high fidelity. High-order schemes overcome computational limitations by computing comparable solutions on grids that are coarser than grids required by a second-order flow solver. The scheme was chosen based on two criteria. The first being that it is well documented in the literature for two-dimensional flow solvers. The second is that the scheme is extendable to the framework used in the Tenasi flow solver developed at the University of Chattanooga SimCenter: National Center for Computational Engineering. The accuracy of the scheme is demonstrated in the following ways: reconstruction of variables from a smooth function, verification by the method of manufactured solutions, and quantitative and qualitative results from the solution of compressible, inviscid flows