Abstract
We present accurate methods for the numerical solution of the Boltzmann equation of rarefied gas. The methods are based on a time splitting technique. On the one hand, the transport is solved by a third-order accurate (in space) Positive and Flux Conservative (PFC) method. On the other hand, the collision step is treated by a Fourier approximation of the collision integral, which guarantees spectral accuracy in velocity, coupled with high-order integrators in time preserving stationary states. Several space dependent numerical tests in 2D and 3D illustrate the accuracy and robustness of the methods.
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Filbet, F., Russo, G. (2004). Accurate numerical methods for the Boltzmann equation. In: Degond, P., Pareschi, L., Russo, G. (eds) Modeling and Computational Methods for Kinetic Equations. Modeling and Simulation in Science, Engineering and Technology. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-0-8176-8200-2_4
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DOI: https://doi.org/10.1007/978-0-8176-8200-2_4
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