Comparative study of certain finiteelement and finitedifference methods in advectiondiffusion simulations
Abstract
The utility of the finiteelement Galerkin technique in advectiondiffusion flow problems is examined by comparison with several finitedifference schemes in one dimension. The calculations show that for relatively coarse grids, finiteelement solutions are either comparable to or significantly better than those obtained from the finitedifference schemes considered. For advectiondominated flows, the superiority of the finiteelement technique is attributed to spatial coupling of timederivative terms inherent in the Galerkin discretization. This procedure, absent from convectional finitedifference schemes, leads to very accurate phase properties for the approximate solution even when coarse grids are used. A twodimensional analogue of the advectiondiffusion problem further illustrates the advantages and accuracy of the finiteelement method in conjunction with the use of isoparametric elements.
 Publication:

NASA STI/Recon Technical Report N
 Pub Date:
 March 1976
 Bibcode:
 1976STIN...7719358L
 Keywords:

 Advection;
 Diffusion Coefficient;
 Finite Difference Theory;
 Finite Element Method;
 Galerkin Method;
 Isoperimetric Problem;
 Matrices (Mathematics);
 Spatial Distribution;
 Fluid Mechanics and Heat Transfer