×

zbMATH — the first resource for mathematics

MUSTA-type upwind fluxes for nonlinear elasticity. (English) Zbl 1159.74046
Summary: The present paper is devoted to the construction and comparative study of upwind methods as applied to the system of one-dimensional nonlinear elasticity equations with particular attention to robustness and accurate resolution of delicate features such as linearly degenerate fields.

MSC:
74S10 Finite volume methods applied to problems in solid mechanics
74B20 Nonlinear elasticity
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Godunov, Journal of Applied Mechanics and Technical Physics 13 pp 868– (1972)
[2] . Elements of Continuum Mechanics and Conservation Laws. Kluwer Academic/Plenum Publishers: Dordrecht/New York, 2003.
[3] Riemann Solvers and Numerical Methods for Fluid Dynamics (2nd edn). Springer: Berlin, 1999.
[4] , . Mathematical Aspects of Numerical Solution of Hyperbolic Systems. Monographs and Surveys in Pure and Applied Mathematics, vol. 118. Chapman & Hall: London, 2002.
[5] Merzhievskii, Combustion, Explosion, and Shock Waves 20 pp 580– (1984)
[6] Merzhievskii, Combustion, Explosion, and Shock Waves 29 pp 744– (1994)
[7] Conservation laws and the symmetric form of equations of nonlinear elasticity theory. Boundary Value Problems for Partial Differential Equations, Proceedings of the Sobolev Seminar, Akademia Nauk USSR, Sibirskoe Otdelenie, Institut Mat., Novosibirsk, vol. 1, 1984; 132–143 (in Russian).
[8] Plohr, Advances in Applied Mathematics 462–493 pp 429– (1992)
[9] Garaizar, Journal of Elasticity 26 pp 43– (1991) · Zbl 0755.73024
[10] Miller, Journal of Computational Physics 167 pp 131– (2001)
[11] Miller, Journal of Computational Physics 193 pp 198– (2003)
[12] Toro, Journal of Computational Physics 216 pp 403– (2006)
[13] Toro EF. MUSTA: a multi-stage numerical, Applied Numerical Mathematics 256 pp 1464– (2006) · Zbl 1101.65088
[14] Titarev, International Journal for Numerical Methods in Fluids 49 pp 117– (2005)
[15] Toro, International Journal for Numerical Methods in Fluids 52 pp 433– (2006)
[16] . Thermodynamics, Conservation Laws, and Symmetric Forms of Differential Equations in Mechanics of Continuous Media. Computational Fluid Dynamics Review, vol. 95. Wiley: New York, 1995; 19–31. · Zbl 0875.73025
[17] Numerical method for 2D equations of nonlinear elasto-plastic Maxwell media. Proceedings of the Institut Math. Akademia Nauk USSR, Sibirskoe Otdelenie, Novosibirsk, vol. 18, 1990; 83–100 (in Russian).
[18] Godunov, Matematicheskii Sbornik 47 pp 357– (1959)
[19] Einfeldt, Journal of Computational Physics 92 pp 273– (1991)
[20] On Glimm-related schemes for conservation laws. Technical Report MMU-9602, Department of Mathematics and Physics, Manchester Metropolitan University, U.K., 1996.
[21] Toro, IMA Journal of Numerical Analysis 20 pp 47– (2000)
[22] Chen, Journal of Hyperbolic Differential Equations 1 pp 531– (2004)
[23] Jiang, Journal of Computational Physics 126 pp 202– (1996)
[24] Quartapelle, Journal of Computational Physics 190 pp 118– (2003)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.