Author : National Aeronautics and Space Adm Nasa
Publisher :
ISBN 13 : 9781729046852
Total Pages : 26 pages
Book Rating : 4.0/5 (468 download)
Book Synopsis Large-Scale Computation of Incompressible Viscous Flow by Least-Squares Finite Element Method by : National Aeronautics and Space Adm Nasa
Download or read book Large-Scale Computation of Incompressible Viscous Flow by Least-Squares Finite Element Method written by National Aeronautics and Space Adm Nasa and published by . This book was released on 2018-10-21 with total page 26 pages. Available in PDF, EPUB and Kindle. Book excerpt: The least-squares finite element method (LSFEM) based on the velocity-pressure-vorticity formulation is applied to large-scale/three-dimensional steady incompressible Navier-Stokes problems. This method can accommodate equal-order interpolations and results in symmetric, positive definite algebraic system which can be solved effectively by simple iterative methods. The first-order velocity-Bernoulli function-vorticity formulation for incompressible viscous flows is also tested. For three-dimensional cases, an additional compatibility equation, i.e., the divergence of the vorticity vector should be zero, is included to make the first-order system elliptic. The simple substitution of 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. To show the validity of this scheme for large-scale computation, we give numerical results for 2D driven cavity problem at Re = 10000 with 408 x 400 bilinear elements. The flow in a 3D cavity is calculated at Re = 100, 400, and 1,000 with 50 x 50 x 50 trilinear elements. The Taylor-Goertler-like vortices are observed for Re = 1,000. Jiang, Bo-Nan and Lin, T. L. and Povinelli, Louis A. Glenn Research Center NCC3-233; RTOP 505-62-21...