Finite difference calculations of buoyant convection in an enclosure: Verification of the nonlinear algorithm
type: Item
instance of: scholarly article
title: Finite difference calculations of buoyant convection in an enclosure: Verification of the nonlinear algorithm
zbMATH Open document ID: 0621.76093
DOI: 10.1016/0168-9274(85)90035-2
author: Ronald G. Rehm
author: P. Darcy Barnett
author: H. R. Baum
author: Daniel M. Corley
published in: Applied Numerical Mathematics
publication date: 1985-01-01T00:00:00Z
review text: Solutions are presented to nonlinear finite difference equations used to represent fire-driven buoyant convection in enclosures. The solutions depend upon the fact that these difference equations permit the decomposition of the discretized velocity field into solenoidal and irrotational components. The irrotational field is shown to satisfy a finite difference analog of Bernoulli's equation when the density is constant. This leads to a three- dimensional time-dependent solution to the difference equations. The solenoidal field is shown to possess steady-state two-dimensional solutions corresponding to a constant non-zero value of the discretized vorticity. The two solutions, together with results presented elsewhere describing finite difference approximations to linear internal waves in enclosures, have been used in the development and testing of the computer-based algorithms used to solve these equations. They have proved particularly useful in assessing the accuracy of finite difference approximations to the equations of inviscid fluid mechanics, as well as in debugging the computer codes implementing these algorithms.
Mathematics Subject Classification ID: 76R05
Mathematics Subject Classification ID: 80A20
Mathematics Subject Classification ID: 76B55
Mathematics Subject Classification ID: 76M99
Mathematics Subject Classification ID: 35Q99
zbMATH DE Number: 4008005
zbMATH Keywords: nonlinear finite difference equations
zbMATH Keywords: fire-driven buoyant convection
zbMATH Keywords: discretized velocity field
zbMATH Keywords: Bernoulli's equation
zbMATH Keywords: three-dimensional time- dependent solution
zbMATH Keywords: solenoidal field
zbMATH Keywords: steady-state two-dimensional solutions
zbMATH Keywords: finite difference approximations
zbMATH Keywords: linear internal waves
zbMATH Keywords: accuracy
MaRDI profile type: Publication
full work available at URL: 0168-9274(85)90035-2
OpenAlex ID: W1992998967
cites work: The equations of motion for thermally driven, buoyant flows
cites work: Finite Difference Calculations of Buoyant Convection in an Enclosure, I. The Basic Algorithm
cites work: The numerical solution of a nonseparable elliptic partial differential equation by preconditioned conjugate gradients
cites work: Finite Difference Solutions for Internal Waves in Enclosures
description: scientific article; zbMATH DE number 4008005