Three-dimensional numerical manifold method for heat conduction problems with a simplex integral on the boundary  

作　　者：TONG DeFu YI XiongWei TAN Fei JIAO YuYong LIANG JiaWei 

机构地区：[1]Faculty of Engineering,China University of Geoscience,Wuhan 430074,China [2]Department of Civil Engineering,Monash University,Melbourne VIC 3800,Australia [3]Badong National Observation and Research Station of Geohazards,China University of Geoscience,Wuhan 430074,China

出　　处：《Science China(Technological Sciences)》2024年第4期1007-1022,共16页中国科学（技术科学英文版）

基　　金：supported by the National Natural Science Foundation of China(Grant Nos.42277165,41920104007,and 41731284);the Fundamental Research Funds for the Central Universities,China University of Geosciences(Wuhan)(Grant Nos.CUGCJ1821 and CUGDCJJ202234);the National Overseas Study Fund(Grant No.202106410040)。

摘　　要：The three-dimensional numerical manifold method(3D-NMM),which is based on the derivation of Galerkin's variation,is a powerful calculation tool that uses two cover systems.The 3D-NMM can be used to handle continue-discontinue problems and extend to THM coupling.In this study,we extended the 3D-NMM to simulate both steady-state and transient heat conduction problems.The modelling was carried out using the raster methods(RSM).For the system equation,a variational method was employed to drive the discrete equations,and the crucial boundary conditions were solved using the penalty method.To solve the boundary integral problem,the face integral of scalar fields and two-dimensional simplex integration were used to accurately describe the integral on polygonal boundaries.Several numerical examples were used to verify the results of 3D steady-state and transient heat-conduction problems.The numerical results indicated that the 3D-NMM is effective for handling 3D both steadystate and transient heat conduction problems with high solution accuracy.

关 键 词：three-dimensional numerical manifold method transient analysis heat conduction problem Galerkin variation simplex integration 

分 类 号：O241.82[理学—计算数学] TK124[理学—数学]