Variational Problems for Some Equations of the Combustion Theory
I. G. Donskoi
Melentiev Energy Systems Institute, Siberian Branch, Russian Academy of Sciences, Irkutsk, 664033, Russia
Keywords: variational methods, equations of reaction-diffusion-convection, thermal explosion, reaction waves
Abstract
Variational formulations are proposed for the equations describing the stationary states of nonisothermal one-dimensional reactors, including those under convective transfer. For the proposed variational formulations, several variants of the numerical solution are considered (based on the method of local variations and the Rayleigh-Ritz method). The features of the use of numerical methods in solving the considered problems are discussed: convergence, the ratio of the spatial grid step to the degree of the approximating polynomial. Modifications of the problem of thermal ignition are considered taking into account convective transfer and heat losses. A variational principle is proposed that determines the structure of the combustion front at a given propagation velocity. It is shown that this variational principle can be used along with the principle of minimum entropy production for a complete solution of the problem of stationary propagation of an exothermic reaction wave.
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