The residual variable method applied to the diffusion equation in cylindrical coordinates
type: Item
instance of: scholarly article
title: The residual variable method applied to the diffusion equation in cylindrical coordinates
zbMATH Open document ID: 0706.35056
DOI: 10.1007/BF01187263
author: Elsie Sterbin Gottlieb
published in: Acta Mechanica
publication date: 1989-01-01T00:00:00Z
review text: We consider a partial differential equation in cylindrical coordinates which describes a dynamic process going on in an infinite medium with an inner cylindrical boundary. If an analytic solution to the problem is not possible to obtain then one would have to resort to numerical techniques. It becomes necessary to discretize the infinite domain even if the solution is required on the inner cylindrical surface only. The numerical difficulties associated with the discretization of an infinite medium are well known. The residual variable method (RVM) is a rigorous method which essentially reduces the number of the spatial dimensions of the problem by one. The governing differential equation is integrated once in the radial direction and, thus, it becomes possible to determine the solution on the inner boundary without having to deal with the infinite domain. In this work, the classical cylindrical diffusion equation is expressed in terms of a residual concentration applying the RVM. Thus, it became possible to eliminate the second derivative of the concentration with respect to the radial coordinate from the diffusion equation. The diffusion on the surface of the cylindrical cavity was studied by considering the cavity surface only. The analytical results obtained from the application of the RVM and the numerical results obtained from the application of the finite difference techniques are compared for the flux at the surface of the region bounded internally by a circular cylinder with zero initial conditions and surface concentration in the form of the Heaviside step function.
Mathematics Subject Classification ID: 35K05
Mathematics Subject Classification ID: 35A35
Mathematics Subject Classification ID: 65M99
Mathematics Subject Classification ID: 65N99
zbMATH DE Number: 4159229
zbMATH Keywords: cylindrical coordinates
zbMATH Keywords: residual variable method
zbMATH Keywords: diffusion equation
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf01187263
OpenAlex ID: W1995817991
description: scientific article; zbMATH DE number 4159229