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A perspective on the numerical solution of convection‐dominated transport problems: A price to pay for the easy way out
Author(s) -
Noorishad J.,
Tsang C. F.,
Perrochet P.,
Musy A.
Publication year - 1992
Publication title -
water resources research
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.863
H-Index - 217
eISSN - 1944-7973
pISSN - 0043-1397
DOI - 10.1029/91wr02730
Subject(s) - upwind scheme , finite element method , space (punctuation) , mathematics , convection , numerical analysis , perspective (graphical) , discontinuous galerkin method , mathematical optimization , convection–diffusion equation , galerkin method , computer science , mechanics , discretization , mathematical analysis , physics , engineering , geometry , structural engineering , operating system
In a brief but fundamental review of the evolution of the conventional numerical techniques used in the solution of convection‐dominated transport problems, we explore the difficulties that have been remedied to various degrees by various workers. In the course of this review we obtain the performance characteristic of the Crank‐Nicolson Galerkin finite element method in the form of a curve in Peclet number and Courant number space. We show that the performance can be altered through a new upwind parameter that can easily be incorporated into many of the existing numerical solution methods. By providing an insight into the limitations of some of these methods we demonstrate, by means of numerical experiments, that the proposed upwinding procedure ensures acceptable solutions throughout the Pe ‐ Cr space at a reasonable cost of the smearing effect.