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arxiv: 1411.7929 · v1 · pith:PBTOA35Onew · submitted 2014-11-28 · 🧮 math.NA

High order semi-Lagrangian methods for the BGK equation

M. Groppi , G. Russo , G. Stracquadanio This is my paper
classification 🧮 math.NA
keywords equationmethodsnumericalschemessemi-lagrangianaccuracyaccurateboltzmann
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A new class of high-order accuracy numerical methods for the BGK model of the Boltzmann equation is presented. The schemes are based on a semi-lagrangian formulation of the BGK equation; time integration is dealt with DIRK (Diagonally Implicit Runge Kutta) and BDF methods; the latter turn out to be accurate and computationally less expensive than the former. Numerical results and examples show that the schemes are reliable and efficient for the investigation of both rarefied and fluid regimes in gasdynamics.

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  1. A meshless MUSCL method for the BGK-Boltzmann equation

    math.NA 2025-12 unverdicted novelty 6.0

    A meshless MUSCL-like method with moving-least-squares discretization and MOOD limiting achieves fourth-order accuracy in 1D and second-order in 2D for BGK simulations on moving domains.