Abstract
Several points have to be emphasized in the direct numerical approach to solving the Boltzmann equation. The direct integration methods contain features intrinsic to computational mathematics based on notions of approximation and convergence. In contrast, for example, to the physical and engineering ideas of Monte Carlo simulation, the direct approaches (besides the obvious physical analogies) appeal originally to clear mathematical images. However, the correct and rigorous proofs of convergence of this discrete scheme solution to the solution of the starting equation is not a simple problem.
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Aristov, V.V. (2001). Main Features of the Direct Numerical Approaches. In: Direct Methods for Solving the Boltzmann Equation and Study of Nonequilibrium Flows. Fluid Mechanics and its Applications, vol 60. Springer, Dordrecht. https://doi.org/10.1007/978-94-010-0866-2_3
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DOI: https://doi.org/10.1007/978-94-010-0866-2_3
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