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Potential and viscous flow problems using the boundary element method

Potential and viscous flow problems using the boundary element method
Potential and viscous flow problems using the boundary element method

This work is concerned with the application of the Boundary Element Method for the solution of steady and transient potential and viscous flow problems. Two-dimensional, axisymmetric and fully three-dimensional problems are considered, the general theory developed and specific numerical procedures derived for each of the above cases.Initially, the derivation of the boundary integral equation equivalent to Laplace's equation is reviewed within the framework of classical potential theory. Numerical procedures for the solution of this equation are discussed, the boundary being discretised by using piecewise constant, linear or quadratic variations for the potential function and its normal derivative.Integral formulations for the solution of the diffusion equationare then studied. Three different approaches are considered: using Laplace transforms, coupling the BEM with the Finite Difference Method or employing time-dependent fundamental solutions. For the latter case, specific numerical procedures for the solution of the time-dependent boundary integral equation equivalent to the diffusion equation are developed and different time-marching schemes tested. Finally, a BEM formulation for the solution of incompressible viscous flow problems governed by the Navier-Stokes equations together with the continuity equation is derived, following Lighthill's vorticity-velocity approach. Numerical procedures for the solution of the resulting set of non-linear integral equations are discussed in detail. Computer programs incorporating several of these features were developed, and examples of applications of such programs are presented throughout this work.

University of Southampton
Wrobel, Luiz Carlos
Wrobel, Luiz Carlos

Wrobel, Luiz Carlos (1981) Potential and viscous flow problems using the boundary element method. University of Southampton, Doctoral Thesis.

Record type: Thesis (Doctoral)

Abstract

This work is concerned with the application of the Boundary Element Method for the solution of steady and transient potential and viscous flow problems. Two-dimensional, axisymmetric and fully three-dimensional problems are considered, the general theory developed and specific numerical procedures derived for each of the above cases.Initially, the derivation of the boundary integral equation equivalent to Laplace's equation is reviewed within the framework of classical potential theory. Numerical procedures for the solution of this equation are discussed, the boundary being discretised by using piecewise constant, linear or quadratic variations for the potential function and its normal derivative.Integral formulations for the solution of the diffusion equationare then studied. Three different approaches are considered: using Laplace transforms, coupling the BEM with the Finite Difference Method or employing time-dependent fundamental solutions. For the latter case, specific numerical procedures for the solution of the time-dependent boundary integral equation equivalent to the diffusion equation are developed and different time-marching schemes tested. Finally, a BEM formulation for the solution of incompressible viscous flow problems governed by the Navier-Stokes equations together with the continuity equation is derived, following Lighthill's vorticity-velocity approach. Numerical procedures for the solution of the resulting set of non-linear integral equations are discussed in detail. Computer programs incorporating several of these features were developed, and examples of applications of such programs are presented throughout this work.

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Published date: 1981

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Local EPrints ID: 459286
URI: http://eprints.soton.ac.uk/id/eprint/459286
PURE UUID: 13b8c473-5f83-4899-84f8-35d673985151

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Date deposited: 04 Jul 2022 17:07
Last modified: 04 Jul 2022 17:57

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Author: Luiz Carlos Wrobel

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