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A novel numerical method for the solution of nonlinear equations with applications to heat transfer

A novel numerical method for the solution of nonlinear equations with applications to heat transfer The purpose of this study is to extend a novel numerical method proposed by the first author, known as the dual mesh control domain method (DMCDM), for the solution of linear differential equations to the solution of nonlinear heat transfer and like problems in one and two dimensions.Design/methodology/approachIn the DMCDM, a mesh of finite elements is used for the approximation of the variables and another mesh of control domains for the satisfaction of the governing equation. Both meshes fully cover the domain but the nodes of the finite element mesh are inside the mesh of control domains. The salient feature of the DMCDM is that the concept of duality (i.e. cause and effect) is used to impose boundary conditions. The method possesses some desirable attributes of the finite element method (FEM) and the finite volume method (FVM).FindingsNumerical results show that he DMCDM is more accurate than the FVM for the same meshes used. Also, the DMCDM does not require the use of any ad hoc approaches that are routinely used in the FVM.Originality/valueTo the best of the authors’ knowledge, the idea presented in this work is original and novel that exploits the best features of the best competing methods (FEM and FVM). The concept of duality is used to apply gradient and mixed boundary conditions that FVM and its variant do not. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png International Journal of Numerical Methods for Heat & Fluid Flow Emerald Publishing

A novel numerical method for the solution of nonlinear equations with applications to heat transfer

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Publisher
Emerald Publishing
Copyright
© Emerald Publishing Limited
ISSN
0961-5539
DOI
10.1108/hff-07-2020-0397
Publisher site
See Article on Publisher Site

Abstract

The purpose of this study is to extend a novel numerical method proposed by the first author, known as the dual mesh control domain method (DMCDM), for the solution of linear differential equations to the solution of nonlinear heat transfer and like problems in one and two dimensions.Design/methodology/approachIn the DMCDM, a mesh of finite elements is used for the approximation of the variables and another mesh of control domains for the satisfaction of the governing equation. Both meshes fully cover the domain but the nodes of the finite element mesh are inside the mesh of control domains. The salient feature of the DMCDM is that the concept of duality (i.e. cause and effect) is used to impose boundary conditions. The method possesses some desirable attributes of the finite element method (FEM) and the finite volume method (FVM).FindingsNumerical results show that he DMCDM is more accurate than the FVM for the same meshes used. Also, the DMCDM does not require the use of any ad hoc approaches that are routinely used in the FVM.Originality/valueTo the best of the authors’ knowledge, the idea presented in this work is original and novel that exploits the best features of the best competing methods (FEM and FVM). The concept of duality is used to apply gradient and mixed boundary conditions that FVM and its variant do not.

Journal

International Journal of Numerical Methods for Heat & Fluid FlowEmerald Publishing

Published: May 24, 2021

Keywords: Dual mesh finite domain method; Nonlinear convection; The finite element method; The finite volume method

References