Two-dimensional radiating gas flow by a moment method

Abstract

T governing equations for multidimensional radiating gas flow, in general, are of a complicated integrodifferential form. Thus, no reasonably simple solutions, valid for the whole range of optical thickness, exist for such problems at the present time. For the limiting cases of an optically thin or thick gas, the integrodifferential equations can be reduced to a system of differential equations, and earlier investigations have been confined to these limits. For onedimensional flow problems, Vincenti and Baldwin suggested the use of an exponential function to approximate the integral term. By this approximation, they were able to obtain a system of purely differential equations that are valid for the whole range of optical thickness. Unfortunately, this technique is not directly applicable to multidimensional flow problems. A different scheme of approximation known as the moment method was first suggested by astrophysicists in problems of transfer of radiation in stars. It was subsequently highly developed by nuclear physicists in dealing with neutron transport problems. Using this scheme of approximation, Traugott and others were able to obtain a system of purely differential equations for one-dimensional flow problems that are valid throughout the whole range of optical thickness. It can be shown that the first approximation in this approach when applied to one-dimensional transfer problems is equivalent to the exponential approximation suggested by Vincenti and Baldwin. In the following, we will apply this technique to multidimensional radiating-gas-flow problems.