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A quasi-two-dimensional benchmark problem for low Mach number compressible codes. (English) Zbl 0913.76060
Summary: We examine a quasi-two-dimensional model problem, which can be used as a benchmark problem for verification of numerical methods for the solution of the low Mach number compressible reactive flow equations. A recently developed high-order splitting method for this type of problem is presented and analyzed, and the behavior of the numerical errors is assessed and compared to asymptotic estimates. It is found that the behavior of splitting errors is predicted well by the asymptotic estimates and that these errors are always smaller than the formal truncation order of the integrating scheme. $$\copyright$$ Academic Press.

##### MSC:
 76M20 Finite difference methods applied to problems in fluid mechanics 76N10 Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics 76V05 Reaction effects in flows 80A32 Chemically reacting flows 92E20 Classical flows, reactions, etc. in chemistry
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