×

zbMATH — the first resource for mathematics

A unified sub-cell force-based discretization for cell-centered Lagrangian hydrodynamics on polygonal grids. (English) Zbl 1429.76089
Summary: We develop a general formalism to derive cell-centered Lagrangian scheme, wherein numerical fluxes are expressed in terms of sub-cell force. The general form of the sub-cell force is obtained by requiring the scheme to satisfy a semi-discrete entropy inequality. Sub-cell force and nodal velocity are computed consistently with cell volume variation by means of a node-centered solver, which results from total energy conservation. Numerical results demonstrate the accuracy and the robustness of this scheme.

MSC:
76N15 Gas dynamics (general theory)
76M12 Finite volume methods applied to problems in fluid mechanics
Software:
CAVEAT
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Després, Lagrangian gas dynamics in two dimensions and Lagrangian systems, Archive for Rational Mechanics and Analysis 178 pp 327– (2005) · Zbl 1096.76046
[2] Carré, A cell-centered Lagrangian hydrodynamics scheme on general unstructured meshes in arbitrary dimension, Journal of Computational Physics 228 (14) pp 5160– (2009) · Zbl 1168.76029
[3] Maire, A cell-centered Lagrangian scheme for two-dimensional compressible flow problems, SIAM Journal on Scientific Computing 224 (2) pp 785– (2007) · Zbl 1251.76028
[4] Maire, A high-order cell-centered Lagrangian scheme for two-dimensional compressible fluid flows on unstructured meshes, Journal of Computational Physics 228 (7) pp 2391– (2009) · Zbl 1156.76434
[5] Maire, Multi-scale Godunov-type method for cell-centered discrete Lagrangian hydrodynamics, Journal of Computational Physics 228 (3) pp 799– (2009) · Zbl 1156.76039
[6] Caramana, The construction of compatible hydrodynamics algorithms utilizing conservation of total energy, Journal of Computational Physics 146 pp 227– (1998) · Zbl 0931.76080
[7] Lax, Systems of conservation laws, Communications on Pure and Applied Mathematics 13 pp 217– (1960) · Zbl 0152.44802
[8] Maire, A cell-centered Arbitrary Lagrangian-Eulerian (ALE) method, International Journal for Numerical Methods in Fluids 56 pp 1161– (2008) · Zbl 1384.76044
[9] Loubère, A subcell remapping method on staggered polygonal grids for Arbitrary-Lagrangian-Eulerian methods, Journal of Computational Physics 209 pp 105– (2005) · Zbl 1329.76236
[10] Ben-Artzi, Generalized Riemann Problems in Computational Fluid Dynamics (2003) · Zbl 1017.76001
[11] Adessio FL Carroll DE Dukowicz JK Harlow FH Johnson JN Kashiwa BA Maltrud ME Ruppel HM CAVEAT: A Computer code for fluid dynamics problems with large distortion and internal slip 1986
[12] Margolin, A discrete operator calculus for finite difference approximations, Computer Methods in Applied Mechanics and Engineering 187 pp 365– (2000) · Zbl 0978.76063
[13] Shashkov, Conservative Finite Difference Methods on General Grids (1996) · Zbl 0844.65067
[14] Botsis, Mécanique des milieux continus (2006)
[15] Rebourcet B http://www-troja.fjfi.cvut.cz/multimat07/presentations/tuesday/Rebourcet_filtering.pdf
[16] Godunov, Résolution numérique des problèmes multidimensionnels de la dynamique des gaz (1979)
[17] Munz, On Godunov-type schemes for Lagrangian gas dynamics, SIAM Journal on Scientific Computing 31 pp 17– (1994) · Zbl 0796.76057
[18] Dukowicz, A general, non-iterative Riemann solver for Godunov’s method, Journal of Computational Physics 61 pp 119– (1984) · Zbl 0629.76074
[19] Kamm JR Timmes FX On efficient generation of numerically robust Sedov solutions 2007
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.