A leastsquares finite element method for 3D incompressible NavierStokes equations
Abstract
The leastsquares finite element method (LSFEM) based on the velocitypressurevorticity formulation is applied to threedimensional steady incompressible NavierStokes problems. This method can accommodate equalorder 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 firstorder 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 (matrixfree) 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 TaylorGortlerlike vortices are observed at Re = 1,000.
 Publication:

31st AIAA Aerospace Sciences Meeting and Exhibit
 Pub Date:
 January 1993
 Bibcode:
 1993aiaa.meetV....J
 Keywords:

 Finite Element Method;
 Incompressible Flow;
 Least Squares Method;
 NavierStokes Equation;
 Three Dimensional Flow;
 Galerkin Method;
 Jacobi Matrix Method;
 Newton Methods;
 Taylor Instability;
 Fluid Mechanics and Heat Transfer