A triangle-based unstructured finite volume method for chemically reactive hypersonic flows. (English) Zbl 0985.76058
Summary: We develop a triangle-based unstructured finite volume method 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 nonlinear 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 two-dimensional numerical test cases illustrates the performance of the method.
MSC:
| 76M12 | Finite volume methods applied to problems in fluid mechanics |
| 76K05 | Hypersonic flows |
| 76V05 | Reaction effects in flows |
| 80A32 | Chemically reacting flows |
Keywords:
chemically reactive flows; \(M\)-matrix theory; hypersonic flows; unstructured grids; triangle-based unstructured finite volume method; Steger-Warming flux-vector splitting approach; implicit multi-stage time marching schemeReferences:
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