Existence, Stability, and Convergence of Solutions of Discrete Velocity Models to the Boltzmann Equation |
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Authors: | Andrzej Palczewski Jacques Schneider |
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Institution: | (1) Department of Mathematics, Warsaw University, 02-097 Warsaw, Poland;;(2) I.S.I.T.V. Option Mathématique, BP 132, 83 957 La Garde Cedex, France; |
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Abstract: | We prove the convergence of finite-difference approximations to solutions of the Boltzmann equation. An essential step is the proof of convergence of discrete approximations to the collision integral. This proof relies on our previous results on the consistency of this approximation. For the space-homogeneous problem we prove strong convergence of our discrete approximation to the strong solution of the Boltzmann equation. In the space-dependent case we prove weak convergence to DiPerna–Lions solutions. |
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Keywords: | Boltzmann-equation discrete velocity models convergence of discrete approximation kinetic theory numerical methods |
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