Bivariate spline method for numerical solution of steady state Navier–Stokes equations over polygons in stream function formulation
✍ Scribed by Ming-Jun Lai; Paul Wenston
- Publisher
- John Wiley and Sons
- Year
- 2000
- Tongue
- English
- Weight
- 347 KB
- Volume
- 16
- Category
- Article
- ISSN
- 0749-159X
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✦ Synopsis
We use the bivariate spline finite elements to numerically solve the steady state Navier-Stokes equations. The bivariate spline finite element space we use in this article is the space of splines of smoothness r and degree 3r over triangulated quadrangulations. The stream function formulation for the steady state Navier-Stokes equations is employed. Galerkin's method is applied to the resulting nonlinear fourth-order equation, and Newton's iterative method is then used to solve the resulting nonlinear system. We show the existence and uniqueness of the weak solution in H 2 (Ω) of the nonlinear fourth-order problem and give an estimate of how fast the numerical solution converges to the weak solution. The Galerkin method with C 1 cubic splines is implemented in MATLAB. Our numerical experiments show that the method is effective and efficient.