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Application of Taylor‐least squares finite element to three‐dimensional advection‐diffusion equation
Author(s) -
Park N.S.,
Liggett J. A.
Publication year - 1991
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.1650130607
Subject(s) - advection , mathematics , finite element method , diffusion , mathematical analysis , upwind scheme , gaussian , convection–diffusion equation , interpolation (computer graphics) , hermite polynomials , geometry , physics , classical mechanics , motion (physics) , quantum mechanics , discretization , thermodynamics
The Taylor‐least squares (TLS) scheme, developed to solve the unsteady advection‐diffusion equation for advection‐dominated cases in one and two dimensions, is extended to three dimensions and applied to some 3D examples to demonstrate its accuracy. The serendipity Hermite element is selected as an interpolation function on a linear hexagonal element. As a validation of the code and as a simple sensitivity analysis of the scheme on the different types of shape functions, the 2D example problem of the previous study is solved again. Four 3D problems, two with advection and two with advection‐diffusion, are also solved. The first two examples are advection of a steep 3D Gaussian hill in rotational flow fields. For the advection‐diffusion problems with fairly general flow fields and diffusion tensors, analytical solutions are obtained using the ray method. Despite the steepness of the initial conditions, very good agreement is observed between the analytical and TLS solutions.