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MATHEMATICS OF COMPUTATION Volume 74, Number 250, Pages 585601
 

Summary: MATHEMATICS OF COMPUTATION
Volume 74, Number 250, Pages 585601
S 0025-5718(04)01715-6
Article electronically published on September 2, 2004
TRIVARIATE SPLINE APPROXIMATIONS
OF 3D NAVIER-STOKES EQUATIONS
GERARD AWANOU AND MING-JUN LAI
Abstract. We present numerical approximations of the 3D steady state Nav-
ier-Stokes equations in velocity-pressure formulation using trivariate splines
of arbitrary degree d and arbitrary smoothness r with r < d. Using func-
tional arguments, we derive the discrete Navier-Stokes equations in terms of B-
coefficients of trivariate splines over a tetrahedral partition of any given polyg-
onal domain. Smoothness conditions, boundary conditions and the divergence-
free condition are enforced through Lagrange multipliers. The pressure is com-
puted by solving a Poisson equation with Neumann boundary conditions. We
have implemented this approach in MATLAB and present numerical evidence
of the convergence rate as well as experiments on the lid driven cavity flow
problem.
1. Introduction
There are many computational methods available in the literature for the numer-

  

Source: Awanou, Gerard - Department of Mathematical Sciences, Northern Illinois University

 

Collections: Mathematics