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A MIXED GREEN ELEMENT FORMULATION FOR THE TRANSIENT BURGERS EQUATION

✍ Scribed by Akpofure E. Taigbenu; Okey O. Onyejekwe

Publisher
John Wiley and Sons
Year
1997
Tongue
English
Weight
200 KB
Volume
24
Category
Article
ISSN
0271-2091

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✦ Synopsis

The transient one-dimensional Burgers equation is solved by a mixed formulation of the Green element method (GEM) which is based essentially on the singular integral theory of the boundary element method (BEM). The GEM employs the fundamental solution of the term with the highest derivative to construct a system of discrete first-order non-linear equations in terms of the primary variable, the velocity, and its spatial derivative which are solved by a two-level generalized and a modified time discretization scheme and by the Newton-Raphson algorithm. We found that the two-level scheme with a weight of 0167 and the modified fully implicit scheme with a weight of 115 offered some marginal gains in accuracy. Three numerical examples which cover a wide range of flow regimes are used to demonstrate the capabilities of the present formulation. Improvement of the present formulation over an earlier BE formulation which uses a linearized operator of the differential equation is demonstrated.

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