A least-squares finite element method for 3D incompressible Navier-Stokes equations
Abstract
The least-squares finite element method (LSFEM) based on the velocity-pressure-vorticity formulation is applied to three-dimensional steady incompressible Navier-Stokes problems. This method can accommodate equal-order interpolations, and results in symmetric, positive definite algebraic system. An additional compatibility equation, i.e., the divergence of vorticity vector should be zero, is included to make the first-order system elliptic. The Newton's method is employed to linearize the partial differential equations, the LSFEM is used to obtain discretized equations, and the system of algebraic equations is solved using the Jacobi preconditioned conjugate gradient method which avoids formation of either element or global matrices (matrix-free) to achieve high efficiency. The flow in a half of 3D cubic cavity is calculated at Re = 100, 400, and 1,000 with 50 x 52 x 25 trilinear elements. The Taylor-Gortler-like vortices are observed at Re = 1,000.
- Publication:
-
31st AIAA Aerospace Sciences Meeting and Exhibit
- Pub Date:
- January 1993
- Bibcode:
- 1993aiaa.meetV....J
- Keywords:
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- Finite Element Method;
- Incompressible Flow;
- Least Squares Method;
- Navier-Stokes Equation;
- Three Dimensional Flow;
- Galerkin Method;
- Jacobi Matrix Method;
- Newton Methods;
- Taylor Instability;
- Fluid Mechanics and Heat Transfer