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Properties of simple model problems for reacting gas flows
Author(s) -
Tegnér J. K.
Publication year - 1994
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.1670170802
Subject(s) - simple (philosophy) , uniqueness , mathematics , action (physics) , dissipation , compressibility , dissipative system , viscosity , stiffness , mathematical analysis , mechanics , thermodynamics , physics , philosophy , epistemology , quantum mechanics
The compressible Navier–Stokes equations for reacting gases are extremely complex. Simpler models have been considered, and for these completely non‐physical propagation speeds have been observed. These model problems are stiff, meaning that several different scales are present in the solution. Numerical solution of non‐reacting flows almost always involves addition of extra dissipation. It will be shown that this action will render a totally wrong propagation speed for a simple model equation of reacting flows. This problem will be accentuated by increasing stiffness of the problem. Existence and uniqueness of a solution to this model equation is proved. The dependence of the propagation speed on the viscosity and a term governing the stiffness (comparable to the reaction rate for a more complete model) is investigated. A remedy for the wrong propagation speed for this simple model equation is proposed such that the speed is correct although the front is smeared out.