ISSN:
0271-2091
Keywords:
Third-order upwind scheme
;
Finite element method
;
Petrov-Galerkin formulation
;
Mixed formulation
;
Engineering
;
Engineering General
Source:
Wiley InterScience Backfile Collection 1832-2000
Topics:
Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
Notes:
A third-order upwind finite element scheme is presented for numerical solutions of incompressible viscous flow problems. In order to achieve the third-order upwind approximation for only the convection term in the Navier-Stokes equations, a simplified Petrov-Galerkin formulation in which a modified weighting function is expressed by the sum of a standard weighting function and its second and third spatial derivatives is employed. The mixed method is also employed in the formulation so that a discretization with high-order accuracy in space is carried out by the use of linear elements. Because a truncation error caused by the third-order upwind approximation is smaller than that of a first-order upwind scheme, it is expected that the third-order upwind scheme will greatly improve the numerical solutions of the Navier-Stokes equations. Numerical results in one and two dimensions are presented to illustrate the effectiveness of the proposed scheme.
Additional Material:
7 Ill.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1002/fld.1650150907
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