Finite Element Modeling for Convection-Diffusion Problems
Abstract
The scope of this study is to develop the basic equations for deriving a finite element formulation which can be used to solve problems related to convection and diffusion dominated flows. The formulation is based on the introduction of a generalized quantity defined as heat displacement. The governing equation is expressed in terms of this quantity and a variational formulation is developed which leads to an equation similar in form to Lagrange's equation of mechanics. This equation may be solved by any numerical method, though it is of particular interest for application of the finite element method. The developed formulation is used to derive two finite element models for solving convection-diffusion boundary value problems. The performance of the two element models is investigated and numerical results are given for different cases of conversion and diffusion with three types of boundary conditions. The numerical results obtained show not only the efficiency of the numerical models to handle pure convection, pure diffusion and mixed convection- diffusion problems but also good stability and accuracy. The applications of the developed numerical models is not limited to diffusion-convection problems but can also be applied to other types of problems such as mass transfer, hydrodynamics and wave propagation. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- May 15, 1980
- Accession Number
- ADA086777
Entities
People
- George A. Keramidas
Organizations
- United States Naval Research Laboratory