비압축성 Navier-Stokes 방정식의 유한요소해석을 위한 선형방정식 반복해법 연구

Abstract

With the aim to simulate environmental fluid flows by the incompressible Navier-Stokes equations, an efficient numerical framework with the finite element method is being developed. In the intermediate stage of development, numerical solution technique to the resulting linear system of algebraic equations is very crucial in obtaining the whole time-dependent and/or nonlinear solution very quickly. In this paper, the primary methodology of the finite element method applied to the Navier-Stokes equations is briefly described. Basic features and convergence behaviors of three iterative solvers - GMRES, Lanczos/ORTHOMIN and Lanczos/ORTHORES algorithm is demonstrated for the FEM induced linear equations. Conclusively, the GMRES algorithm show no oscillatory convergence property, but is very slow to get accurate numerical solution with a considerable accuracy level. On the other hand, the Lanczos/ORTHOMIN and Lanczos/ORTHORES algorithm are very fast in spite of rough fluctuations in the residual norms.