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Second-Order Invariant Domain Preserving Approximation of the Euler Equations Using Convex Limiting
Texas A&M Univ, Dept Math, College Stn, TX 77843 USA.
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Computational Science.
Texas A&M Univ, Dept Math, College Stn, TX 77843 USA.
Texas A&M Univ, Dept Math, College Stn, TX 77843 USA.
2018 (English)In: SIAM Journal on Scientific Computing, ISSN 1064-8275, E-ISSN 1095-7197, Vol. 40, no 5, p. A3211-A3239Article in journal (Refereed) Published
Abstract [en]

A new second-order method for approximating the compressible Euler equations is introduced. The method preserves all the known invariant domains of the Euler system: positivity of the density, positivity of the internal energy, and the local minimum principle on the specific entropy. The technique combines a first-order, invariant domain preserving, guaranteed maximum speed method using a graph viscosity (GMS-GV1) with an invariant domain violating, but entropy consistent, high-order method. Invariant domain preserving auxiliary states, naturally produced by the GMS-GV1 method, are used to define local bounds for the high-order method, which is then made invariant domain preserving via a convex limiting process. Numerical tests confirm the second-order accuracy of the new GMS-GV2 method in the maximum norm, where the 2 stands for second-order. The proposed convex limiting is generic and can be applied to other approximation techniques and other hyperbolic systems.

Place, publisher, year, edition, pages
SIAM PUBLICATIONS , 2018. Vol. 40, no 5, p. A3211-A3239
Keywords [en]
hyperbolic systems, Riemann problem, invariant domain, entropy inequality, high-order method, exact rarefaction, quasi-convexity, limiting, finite element method
National Category
Computational Mathematics
Identifiers
URN: urn:nbn:se:uu:diva-369441DOI: 10.1137/17M1149961ISI: 000448803100016OAI: oai:DiVA.org:uu-369441DiVA, id: diva2:1270800
Available from: 2018-12-14 Created: 2018-12-14 Last updated: 2019-01-22Bibliographically approved

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Nazarov, Murtazo

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