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Steady and unsteady finite element analysis of incompressible viscous fluid
Author(s) -
Kawahara Mutsuto,
Yoshimura Nobutoshi,
Nakagawa Katsuya,
Ohsaka Hajime
Publication year - 1976
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1620100213
Subject(s) - finite element method , mathematics , discretization , galerkin method , compressibility , perturbation (astronomy) , numerical analysis , mathematical analysis , incompressible flow , newton's method , boundary value problem , pressure correction method , mixed finite element method , flow (mathematics) , mechanics , physics , geometry , nonlinear system , thermodynamics , quantum mechanics
Finite element procedures and related illustrative numerical examples for incompressible viscous fluid motion are discussed in this paper. The steady flow problem is solved by the Newton–Raphson method and the perturbation method. By numerical examples, it can be shown that the combined use of the Newton–Raphson method and perturbation method is suitable. For the analysis of unsteady flow, the perturbation method is employed. Assuming that the basic flow is known, unsteady flow is calculated by accumulating the solution of the linearized equation in which the boundary values are varied by small amounts. Steady flows of temperature dependent free convection are also discretized and analyzed by the same procedure as the conventional finite element Galerkin method. For shape functions, quadratic polynomials are used for velocity and temperature, and linear polynomials for pressure. It is to be noted that the selections of shape functions and solution method are the keys to the analysis of highly non‐linear fluid flow problems such as those discussed in this paper.