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Space–time elements for the shock wave propagation problem
Author(s) -
Cella A.,
Lucchesi M.,
Pasquinelli G.
Publication year - 1980
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1620151005
Subject(s) - classification of discontinuities , shock wave , computation , shock (circulatory) , finite element method , nonlinear system , space (punctuation) , numerical integration , spacetime , simple (philosophy) , numerical analysis , mathematics , discontinuity (linguistics) , mathematical analysis , computer science , physics , mechanics , algorithm , medicine , philosophy , epistemology , quantum mechanics , thermodynamics , operating system
A space–time finite element procedure is presented that integrates on time the equations of nonlinear dynamics. When a shock occurs and subsequently propagates, the space–time procedure gives accurate and stable numerical results, without after‐shock wiggling, at relatively low costs of computation. The procedure is implicit. The good performance is to be attributed to the capability of the space‐time elements to cope with discontinuities in the velocity by the simple use of reduced numerical integration. The numerical solution of the Fermi–Pasta–Ulam problem is discussed.