[2408.16105] SAV-based entropy-dissipative schemes for a class of kinetic equations
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Mathematics > Numerical Analysis

arXiv:2408.16105 (math)
[Submitted on 28 Aug 2024 (v1), last revised 30 Aug 2024 (this version, v2)]

Title:SAV-based entropy-dissipative schemes for a class of kinetic equations

Authors:Shiheng Zhang, Jie Shen, Jingwei Hu
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Abstract:We introduce novel entropy-dissipative numerical schemes for a class of kinetic equations, leveraging the recently introduced scalar auxiliary variable (SAV) approach. Both first and second order schemes are constructed. Since the positivity of the solution is closely related to entropy, we also propose positivity-preserving versions of these schemes to ensure robustness, which include a scheme specially designed for the Boltzmann equation and a more general scheme using Lagrange multipliers. The accuracy and provable entropy-dissipation properties of the proposed schemes are validated for both the Boltzmann equation and the Landau equation through extensive numerical examples.
Comments: 20 pages, 6 figures
Subjects: Numerical Analysis (math.NA)
Cite as: arXiv:2408.16105 [math.NA]
  (or arXiv:2408.16105v2 [math.NA] for this version)
  https://doi.org/10.48550/arXiv.2408.16105

Submission history

From: Shiheng Zhang [view email]
[v1] Wed, 28 Aug 2024 19:24:54 UTC (3,776 KB)
[v2] Fri, 30 Aug 2024 01:33:13 UTC (3,777 KB)
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