Two-dimensional numerical manifold method for heat conduction problems. (April 2022)

• Record Type: Journal Article
• Authors: Tan, Fei; Tong, Defu; Liang, Jiawei; Yi, Xiongwei; Jiao, Yu-Yong; Lv, Jiahe
• Is Part Of: Engineering analysis with boundary elements. Volume 137(2022)
• Page Start: 119
• Page End: 138
• Publication Date: 2022-04
• Subjects: Heat conduction problem -- Transient analysis -- Galerkin variation -- Numerical manifold method; Boundary element methods -- Periodicals; Engineering mathematics -- Periodicals; Équations intégrales de frontière, Méthodes des -- Périodiques; Mathématiques de l'ingénieur -- Périodiques; Boundary element methods; Engineering mathematics; Periodicals; 620.00151
• DOI: 10.1016/j.enganabound.2022.02.004
• Languages: English
• ISSNs: 0955-7997

Abstract

Abstract: The numerical manifold method (NMM) is a calculation method based on Galerkin's variation and contains a dual covering system. Therefore, the NMM can easily deal with the construction of high-order manifold elements and is convenient for adaptive analysis. This study employed the NMM to simulate steady-state and transient heat conduction problems. The system equations were derived and a penalty function method was applied to deal with the boundary conditions. By simulating calculation examples for a one-dimensional bar, cuboid rock specimens, and thick-walled cylinders, the process of solving steady-state and transient heat-conduction problems and the influence law of the temperature pattern are demonstrated. Moreover, the convergence and effectiveness of the NMM in handling two-dimensional (2D) steady-state and 2D transient heat conduction problems was verified.