Accession Number : ADA117110

Title :   Variational Analysis and Approximate Solutions for Transport Phenomena.

Descriptive Note : Memorandum rept.,

Corporate Author : NAVAL RESEARCH LAB WASHINGTON DC

Personal Author(s) : Keramidas,George A

PDF Url : ADA117110

Report Date : 30 Jun 1982

Pagination or Media Count : 83

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)

Descriptors :   *Partial differential equations, *Variational methods, *Approximation(Mathematics), *Transport properties, *Heat transfer, *Fluid dynamics, Solutions(General), Mechanics, Lagrangian functions, Finite element analysis, Parameters, Coordinates, Linearity, Expansion, Advection, Convection, Diffusion, Mass transfer, Numerical methods and procedures, Displacement, Error analysis, Convergence, Boundary value problems

Subject Categories : Numerical Mathematics
      Fluid Mechanics
      Thermodynamics

Distribution Statement : APPROVED FOR PUBLIC RELEASE