ISSN:
0029-5981
Keywords:
Engineering
;
Engineering General
Source:
Wiley InterScience Backfile Collection 1832-2000
Topics:
Mathematics
,
Technology
Notes:
A new non-diffusive Petrov-Galerkin type finite element method which uses test functions two polynomial degrees higher than the trial functions is developed for the transient convection dominated transport equation in two dimensions. The scheme uses bilinear quadrilateral finite elements for the spatial discretization and Crank-Nicolson finite differencing for the time integration. The standard product extension of very successful one-dimensional N + 2 degree upwinding functions to two dimensions is ineffective for general 2-D flow problems, especially at higher Courant numbers where cross-derivative truncation terms become important. Therefore effective N + 2 degree test functions are developed through an analysis by which the truncation error terms in the discrete nodal equation are eliminated up to fifth order. The new scheme is very effective for general 2-D flows over a wide Courant number range and eliminates the troublesome cross-derivative truncation terms. The scheme is simple and robust in that the upwinding coefficients are readily defined and only dependent on Courant number. Numerical examples illustrate the excellent behaviour of the new scheme.
Additional Material:
15 Ill.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1002/nme.1620300302
