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Simplified equations for low Mach number combustion with strong heat release. (English) Zbl 0751.76068
Dynamical issues in combustion theory, Proc. Workshop, Minneapolis/MN (USA) 1989, IMA Vol. Math. Appl. 35, 167-211 (1991).
[For the entire collection see Zbl 0742.00074.]
We present a limiting system of equations which describe combustion processes with strong heat release at low Mach numbers in either confined or unbounded regions. This limiting system of equations allows for large heat release, substantial temperature and density variation, and substantial interaction with the hydrodynamic flow field including the effects of turbulence. Nevertheless, since the detailed effects of the nonlinear acoustic waves have been removed, this zero Mach number limiting system is significantly simpler than the complete system of equations of compressible combustion. In this paper, we also explicitly compute and analyze a number of exact solutions of these equations in simple geometries. These solutions illustrate the effects of confinement, curvature, external piston motion, and vorticity production of both the combustion process and the hydrodynamic flow field.
One of the goals of this paper is to stimulate the interest of workers in theoretical combustion and nonlinear P.D.E.’s in a new class of problems involving reaction-diffusion equations coupled with fluid dynamics.

76V05 Reaction effects in flows
35K57 Reaction-diffusion equations
80A25 Combustion