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首页> 外文期刊>International journal of numerical methods for heat & fluid flow >A novel numerical method for the solution of nonlinear equations with applications to heat transfer
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A novel numerical method for the solution of nonlinear equations with applications to heat transfer

机译：一种新的数值方法，用于加热施用的非线性方程溶液

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摘要

Purpose - 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/approach - In 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). Findings - Numerical 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/value - To 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.
机译：目的 - 本研究的目的是扩展第一作者提出的新型数值方法，称为双网格控制域方法（DMCDM），用于线性微分方程解决非线性传热溶液和类似问题的方法一个和两个维度。设计/方法/方法 - 在DMCDM中，有限元的网格用于变量的近似值和用于控制域的另一个网格，以满足控制方程的满足。两个网格都完全覆盖域，但有限元网格的节点位于控制域的网格内。 DMCDM的突出特征是二元性的概念（即原因和效果）用于施加边界条件。该方法具有有限元方法（FEM）和有限体积法（FVM）的一些理想的属性。调查结果 - 数值结果表明，他DMCDM比使用的相同网格的FVM更准确。此外，DMCDM不需要使用在FVM中常规使用的任何临时方法。原创性/价值 - 据作者的知识，在这项工作中提供的想法是原创的，是利用最佳竞争方法（FEM和FVM）的最佳特征的新颖。二元性的概念用于应用FVM及其变体的梯度和混合边界条件。

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