Variational Analysis and Approximate Solutions for Transport Phenomena.

Abstract

Certain concepts of classical mechanics are utilized to derive the variational formulation for a field partial differential equation. By introducing suitable parameters, it is demonstrated that the concepts of virtual work and generalized coordinates can be extended to the general transport equation and this equation can be translated into Lagrange's equations of mechanics. The system of equations may represent a large number of physical processes and it is not restricted by any means to a particular problem. The Lagrangian system of equations is most suitable for deriving approximate solutions and this is demonstrated by assuming a linear series expansion in terms of the generalized coordinates. Furthermore, it is shown that approximate methods, such as the finite element method, can be directly derived as a special application of the generalized approach. Examples of approximate solutions are given for some typical problems encountered in transport processes. (Author)

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Document Details

Document Type
Technical Report
Publication Date
Jun 30, 1982
Accession Number
ADA117110

Entities

People

  • George A. Keramidas

Organizations

  • United States Naval Research Laboratory

Tags

Communities of Interest

  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Boltzmann Equation
  • Boundary Value Problems
  • Cartesian Coordinates
  • Coefficients
  • Convection
  • Coordinate Systems
  • Differential Equations
  • Energy
  • Equations
  • Finite Element Analysis
  • Heat Transfer
  • Mechanics
  • Molecular Mechanics Methods
  • Partial Differential Equations
  • Transport Ships
  • Variational Equations
  • Variational Principles

Readers

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