Finite element least square methods for problems of mixed-type
Abstract
A finite-element method of steady-relaxation type which uses a least-squares formulation to transform hyperbolic problems to elliptic problems (Chattot, 1980) is applied to four steady-flow problems. A primary advantage of the least-squares method (LSM) is that it eliminates the need for mixed schemes and permits the use of centered scheme regardless of the local type of the system. The problems analyzed are the linear hyperbolic convection equation, Tricomi's mixed-type equation, the nonlinear isentropic transonic flow problem, and the full steady Euler equations of transonic plane-nozzle flow with nonisentropic shocks. The incomplete-Cholesky-conjugate-gradient method is used to solve the discrete systems. Results are presented in graphs, and the convergence behavior is discussed.
- Publication:
-
Finite Element Flow Analysis
- Pub Date:
- 1982
- Bibcode:
- 1982fefa.proc.1071B
- Keywords:
-
- Computational Fluid Dynamics;
- Finite Element Method;
- Least Squares Method;
- Transonic Flow;
- Convection;
- Euler Equations Of Motion;
- Isentropic Processes;
- Fluid Mechanics and Heat Transfer