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The influence of a source term, an example: chemically reacting hypersonic flow

by M. Fey and R. Jeltsch and S. Müller

(Report number 1992-06)

Abstract
We show, by way of an example, that the solution of a system of hyperbolic conservation laws exhibits an unexpected behavior if a source term is present. The example is the system of Euler equations for N species in two space dimensions. If the source term is not present and in the initial and inflow conditions a fixed mixture of species is prescribed then the solution basically behaves like the flow of an ideal gas, except that there are additional equations for the different species. However, introducing the chemical reaction terms produces a thin boundary layer, which makes numerical computations of the two-dimensional problem extremely difficult, if not impossible for todays computers. In addition this boundary layer is unphysical. We shall analyse the boundary layer in a one-dimensional calculation along the stagnation point stream line. In M. Fey and R. Jeltsch, in Proceedings of the 9th GAMM Conference on Numerical Methods in Fluid Dynamics, a modification of the Van Leer flux vector splitting is presented which is able to indicate the presence of the boundary layer in a two-dimensional calculation.

Keywords: chemical boundary layer, geometrical singularities

@Techreport{FJM92_16,
  author = {M. Fey and R. Jeltsch and S. M\"uller},
  title = {The influence of a source term, an example: chemically reacting hypersonic flow},
  institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich},
  number = {1992-06},
  address = {Switzerland},
  url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports1992/1992-06.pdf },
  year = {1992}
}

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