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)

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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

Tags

DTIC Thesaurus Topics

  • Accuracy
  • Boundaries
  • Boundary Value Problems
  • Coefficients
  • Computational Fluid Dynamics
  • Computational Science
  • Convection
  • Differential Equations
  • Diffusion
  • Equations
  • Finite Element Analysis
  • Mechanics
  • Plastic Explosives
  • Sine Waves
  • Wave Propagation
  • Waveforms
  • Waves

Fields of Study

  • Mathematics

Readers

  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)