A Triangle-Based Unstructured Finite-Volume Method for Chemically Reactive Hypersonic Flows

A triangle-based unstructured finite-volume method is developed for chemically reactive hypersonic calculations. The method is based on a Steger–Warming flux-vector splitting approach generalized to mixtures of thermally perfect gases. Second-order-in-space and time accuracy is provided by limited flux blending and an implicit multi-stage time marching scheme. The final stiff non-linear problem resulting from discretization presents a very peculiar block diagonal structure. This allows a decoupling of the species and gas dynamic equations in smaller subproblems. A linear algebra argument based on M-matrix theory makes it possible also to show that the method guarantees positivity of species mass densities and vibrational energies under a reasonable CFL-like constraint. Finally, a set of 2-D numerical test cases illustrates the performance of the method.