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Synchronized flux limiting for gas dynamics variables. (English) Zbl 1373.76286

Summary: 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.

MSC:

76N15 Gas dynamics (general theory)
76L05 Shock waves and blast waves in fluid mechanics

Software:

SHASTA
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Full Text: DOI

References:

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