Synchronized flux limiting for gas dynamics variables

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• 作者：Christoph Lohmann ^{christoph.lohmann@math.tu-dortmund.de" class="auth_mail" title="E-mail the corresponding author} ; Dmitri Kuzmin ; ^{kuzmin@math.uni-dortmund.de" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Systems of conservation laws ; Local extremum diminishing limiters ; Positivity preservation ; Flux-corrected transport/remapping
• 刊名：Journal of Computational Physics
• 出版年：2016
• 出版时间：1 December 2016
• 年：2016
• 卷：326
• 期：Complete
• 页码：973-990
• 全文大小：2283 K

文摘

This work addresses the design of failsafe flux limiters for systems of conserved quantities and derived variables in numerical schemes for the equations of gas dynamics. Building on Zalesak's multidimensional flux-corrected transport (FCT) algorithm, we construct a new positivity-preserving limiter for the density, total energy, and pressure. The bounds for the underlying inequality constraints are designed to enforce local maximum principles in regions of strong density variations and become less restrictive in smooth regions. The proposed approach leads to closed-form expressions for the synchronized correction factors without the need to solve inequality-constrained optimization problems. A numerical study is performed for the compressible Euler equations discretized using a finite element based FCT scheme.