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

Enrico Bertolazzi and Gianmarco Manzini


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 sub problems. A linear algebra argument based on M-matrix theory allows 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.


Hypersonic Flows, Unstructured Grids, Finite Volumes, Semi-implicit schemes, M-matrix.

DOI: https://www.doi.org/10.1006/jcph.2001.6644