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Discretization schemes of advection term in the finite element method for incompressible Navier-Stokes equation

Uchiyama T.

Applied Mechanics and Engineering

1998

Vol. 3, no 1

39-53

In a finite element method for an incompressible Navier-Stokes equation, the divergent, gradient, simplified, and mixed schemes are applicable to discretize the advection term. The simplified scheme substitutes the average velocity in each element for the advection velocity, and the mixed scheme is a combination of the divergent and gradient schemes. This paper investigates the effects of these schemes on the computational accuracy and CPU time of a finite element method based on the SMAC method. The investigations are accomplished by solving the flow in a square cavity for the cases in which the velocity field is calculated by the mass-lumping and multi-pass algorithms. The computational accuracy is higher in the order of divergent, mixed, gradient, and simplified schemes, irrespective of the solution algorithms for the velocity. The divergent scheme, allowing calculation with the shortest CPU time, is the most useful among the four schemes. The improvement in computational accuracy produced by the multi-pass algorithm is independent of the discretization scheme of the advection term.