Thermal nonequilibrium modeling using the direct simulation Monte Carlo method: Application to rotational energy

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Abstract
Individual probabilities of energy exchange, appearing in the Boltzmann equation, are proposed. They are developed, for a continuous internal energy, to reproduce, on average, the expected relaxation times. The problem consists in linking the required individual probability to the relaxation time to be reproduced. It is stated, for a given collisional model, from the Boltzmann equation collisional kernel. The underlying assumptions are put forward. A new and systematic resolution method, based on the Laplace transformation, is then presented in detail. Illustrations are proposed, within the frame of the direct simulation Monte Carlo method of Bird, investigating two collisional models. The first one is the widely used variable hard sphere model. Next, an original application to the generalized hard sphere model is also performed. Examples of resolutions are carried out studying rotational relaxation. The rotational models previously developed are included in the results obtained. A new hypothesis used to state the problem is discussed in the light of numerical calculations and of a recent mathematical study.