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From Wikipedia, the free encyclopedia
Majda's model is a qualitative model (in mathematical physics) introduced by Andrew Majda in 1981 for the study of interactions in the combustion theory of shock waves and explosive chemical reactions.[1]
The following definitions are with respect to a Cartesian coordinate system with 2 variables. For functions , of one spatial variable representing the Lagrangian specification of the fluid flow field and the time variable , functions , of one variable , and positive constants , the Majda model is a pair of coupled partial differential equations:[2]
Since its introduction in the early 1980s, Majda's simplified "qualitative" model for detonation ... has played an important role in the mathematical literature as test-bed for both the development of mathematical theory and computational techniques. Roughly, the model is a system consisting of a Burgers equation coupled to a chemical kinetics equation. For example, Majda (with Colella & Roytburd) used the model as a key diagnostic tool in the development of fractional-step computational schemes for the Navier-Stokes equations of compressible reacting fluids ...[3]
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