Conservative Averaging As An Approximate
Method For Solution Of Some Direct And Inverse
Heat Transfer Problems
Author(s)
A. Buikis
Abstract
The conservative averaging method was developed as an approximate analytical
and/or numerical method for solving partial differential equation or its system
with piece-wise constant (continuous) coefficients. The usage of this
approximate method for separate relatively thin sub-domain or/and for subdomain
with al large heat conduction coefficient leads to a reduction of domain
in which the solution must be found. To apply this method for all sub-domains of
layered media, a special type of spline was constructed: the integral averaged
values interpolating parabolic spline. The usage of this spline allows diminishing
the dimensions of initial problem per one. It is important that in all cases the
original problem with discontinuous coefficients from Rn+1 transforms to
problem with continuous coefficients in Rn. A method of conservative averaging
for ill-posed inverse problems in some cases allows transforming them to wellposed
inverse problems.
Keywords: heat transfer, piecewise constant (continuous) coefficients,
conservative averaging, non-classical conditions, integral spline, mesh
(dimension) reduction, direct problem, inverse problem.
1 Introduction
By modeling practically interesting processes, e.g. heat transfer processes in
non-homogeneous media, very often we need to consider the situation, when the
medium has an organized structure, i.e. it is not fully chaotic. For example it
often has a layered structure. In addition some of these layers are relatively thin
in comparison with adjacent layers and have strongly different physical
properties.
Keywords
heat transfer, piecewise constant (continuous) coefficients,conservative averaging, non-classical conditions, integral spline, mesh(dimension) reduction, direct problem, inverse problem.
Related Book
Other papers in this volume
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