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Utilization of the method of characteristics to solve accurately two‐dimensional transport problems by finite elements
Author(s) -
Varoḡlu Erol,
Finn W. D. Liam
Publication year - 1982
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/fld.1650020205
Subject(s) - convection–diffusion equation , advection , finite element method , diffusion , mathematics , dispersion (optics) , method of mean weighted residuals , courant–friedrichs–lewy condition , residual , convection , space (punctuation) , feature (linguistics) , mathematical analysis , numerical analysis , mathematical optimization , mechanics , algorithm , computer science , physics , discretization , galerkin method , linguistics , philosophy , optics , thermodynamics , operating system
A new finite element method is presented for the solution of two‐dimensional transport problems. The method is based on a weighted residual formulation in which the method of characteristics is combined with the finite element method. This is achieved by orienting sides of the space‐time elements joining the nodes at subsequent time levels along the characteristics of the pure advection equation associated with the transport problem. The method is capable of solving numerically the advection‐‐diffusion equation without generating oscillations or numerical diffusion for the whole spectrum of dispersion from diffusion only through mixed dispersion to pure convection. The utility and accuracy of the method are demonstrated by a number of examples in two space dimensions and a comparison of the numerical results with the exact solution is presented in one case. A very favourable feature of the method is the capability of solving accurately advection dominated transport problems with very large time steps for which the Courant number is well over one.