An approximate Boltzmann equation, known as the single relaxation model is studied here. This equation is linearized and the fundamental solution is considered. Following N. Grad, the solution, asymptotic in small values of the ratio of mean-free-path to distance from the origin, is sought. It can be shown that the fundamental solution itself gives the asymptotic description of the flow field past an object. This solution gives the asymptotic description when the distance from the origin is much greater than either the mean-free-path or the body size. This is true independently of the Knudsen number.
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Atomic Energy Commission Report NYO-9086
Description
An approximate Boltzmann equation, known as the single relaxation model is studied here. This equation is linearized and the fundamental solution is considered. Following N. Grad, the solution, asymptotic in small values of the ratio of mean-free-path to distance from the origin, is sought. It can be shown that the fundamental solution itself gives the asymptotic description of the flow field past an object. This solution gives the asymptotic description when the distance from the origin is much greater than either the mean-free-path or the body size. This is true independently of the Knudsen number.
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