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Hybrid Methods in Engineering

ISSN Imprimer: 1099-2391
ISSN En ligne: 2641-7359

Archives: Volume 1, 1999 to Volume 4, 2002

Hybrid Methods in Engineering

DOI: 10.1615/HybMethEng.v2.i2.60
13 pages

THREE GREEN ELEMENT FORMULATIONS FOR BURGERS' EQUATION

Akpofure E. Taigbenu
Department of Civil & Water Engineering, National University of Science & Technology, Bulawayo, Zimbabwe

RÉSUMÉ

Burgers' equation, which provides a useful model for many diverse and seemingly unrelated phenomena such as shock flows, turbulence, wave propagation in combustion chambers, vehicular traffic movement, and acoustic transmission, is simulated with three formulations of the Green element method (GEM), and their results are compared. The Green element method is a novel way of implementing the singular boundary integral theory so that the theory is of more general application, and a banded global coefficient is achieved, thereby enhancing ease of its inversion and computational efficiency. These formulations are obtained essentially by using three Green's functions along a unified approach that achieves an integral representation of the differential operator via Green's identity, and numerically implements that integral representation element by element. The resultant discretized element equations are recursive, allowing for the transient history of the solution to be obtained at discrete time intervals. Because the Green's function of the first formulation does not have the time variable, the treatment of the temporal derivative is done by a generalized two-level difference approximation. The discretized element equations are nonlinear, requiring further simplification of linearization either by the Newton-Raphson or Picard algorithm. With three numerical examples, it is shown that the first formulation gives optimal results at about twice the computing time of the second formulation, which is fastest in computing speed.


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