Finite element analysis of natural convection with penalty function method
Abstract
The penalty-function finite-element algorithm of Miyauchi et al. for steady-state natural convection is extended to time-dependent problems and turbulent flows. The basic equations are set forth; the penalty-function formulation is derived; and the discretization is explained. The time-dependent equation is integrated implicitly with variable time intervals, and the mixing-length hypothesis of Prandtl (1945) is used in the analysis of turbulence. Natural convection in a closed cavity and turbulent boundary-layer flow along a perpendicular hot plate are calculated, and the results are presented in graphs and found to agree with those of Zienkiewicz et al. (1975) and Eckert and Jackson (1951).
- Publication:
-
Finite Element Flow Analysis
- Pub Date:
- 1982
- Bibcode:
- 1982fefa.proc..287M
- Keywords:
-
- Computational Fluid Dynamics;
- Finite Element Method;
- Free Convection;
- Penalty Function;
- Turbulent Flow;
- Boundary Value Problems;
- Discrete Functions;
- Incompressible Fluids;
- Mixing Length Flow Theory;
- Momentum Theory;
- Navier-Stokes Equation;
- Time Dependence;
- Wall Flow;
- Fluid Mechanics and Heat Transfer