Reduction of modes for the solution of inverse natural convection problems
type: Item
instance of: scholarly article
title: Reduction of modes for the solution of inverse natural convection problems
zbMATH Open document ID: 0999.76123
DOI: 10.1016/S0045-7825(99)00453-3
author: R. Smith
published in: Computer Methods in Applied Mechanics and Engineering
publication date: 2002-12-02T00:00:00Z
review text: The authors consider an inverse convection problem of determining the wall heat flux from the temperature measurement within the flow. The unknown heat flux is at the bottom wall of a two-dimensional cavity. The performance function, which is the sum of squared residuals between calculated and observed temperature, is minimized by using the conjugate gradient method. The authors use a Karhunen-Loève-Galerkin method which is a type of Galerkin method that employs the empirical eigenfunctions of Karhunen-Loève decomposition as basis functions. This allows to reduce the governing nonlinear partial differential equations to the minimal number of ordinary differential equations by limiting the solution space to the smallest linear subspace that is sufficient to describe the observed phenomena. This reduction is important, because the techniques for inverse problems are basically iterative, and otherwise the solution of the present inverse natural convection problem requires repeated numerical solutions of Boussinesq equation and its adjoint equation, which is daunting even with the modern high-speed computers.
reviewed by: Ioan Pop
Mathematics Subject Classification ID: 76R10
Mathematics Subject Classification ID: 76M25
Mathematics Subject Classification ID: 80A20
Mathematics Subject Classification ID: 80A23
zbMATH DE Number: 1563789
zbMATH Keywords: inverse natural convection problems
zbMATH Keywords: wall heat flux
zbMATH Keywords: two-dimensional cavity
zbMATH Keywords: conjugate gradient method
zbMATH Keywords: Karhunen-Loève-Galerkin method
zbMATH Keywords: empirical eigenfunctions
zbMATH Keywords: Karhunen-Loève decomposition
zbMATH Keywords: basis functions
zbMATH Keywords: ordinary differential equations
zbMATH Keywords: linear subspace
MaRDI profile type: Publication
cites work: An efficient computational method of boundary optimal control problems for the Burgers equation
cites work: Boundary control of the Navier-Stokes equation by empirical reduction of modes
cites work: Q4137920
cites work: A general optimization method using adjoint equation for solving multidimensional inverse heat conduction
cites work: Pseudospectral methods for solution of the incompressible Navier-Stokes equations
cites work: Q3999241
cites work: Function minimization by conjugate gradients
full work available at URL: s0045-7825(99)00453-3
OpenAlex ID: W2044013161
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description: scientific article; zbMATH DE number 1563789