Matrix free meshless method for transient heat conduction problems |
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| Authors: | Xiao Hua Zhang Jie Ouyang Lin Zhang |
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| Affiliation: | 1. Hefei University of Technology, China;2. Pennsylvania State University, United States;3. University of Science and Technology of China, China;4. SINOPEC Research Institute of Petroleum Engineering, China;1. Economides Consultants Inc., United States;2. University of Houston, TX, United States;1. School of Mathematics, University of Manchester, Manchester M13 9PL, United Kingdom;2. DAMTP, Wilberforce Road, Cambridge CB3 OWA, United Kingdom;1. Texas A&M University, 3116 TAMU–907 Richardson Building, College Station, TX 77843, United States;2. Texas A&M University, 3116 TAMU – 401 J Richardson Building, College Station, TX 77843, United States;3. Texas A&M University, 13088 South Dowling Road, College Station, TX 77845-6806, United States;1. Beijing Key Laboratory of Unconventional Natural Gas Geological Evaluation and Development Engineering, School of Energy Resources, China University of Geosciences, Beijing 100083, China;2. Exploration Research Institute, Anhui Provincial Bureau of Coal Geology, Hefei, Anhui 230088, China;3. School of Engineering, University of Aberdeen, Aberdeen, AB24 3UE, UK;4. Research Institute of Petroleum Exploration and Development, PetroChina, Beijing 100083, China;5. Hubei Subsurface Multi-Scale Imaging Key Laboratory, Institute of Geophysics and Geomatics, China University of Geosciences, Wuhan 430074, China |
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| Abstract: | In the paper, the element free Galerkin method (EFGM) is applied to calculate two-dimensional unsteady state heat conduction problems. As is well known, most of the meshless methods have higher computational cost than that of finite element method (FEM). In order to overcome this shortcoming especially for transient heat conduction problems, mass lumping procedure is adopted in EFGM, which can decrease the computational cost evidently. Moreover, this technique which can simplify the solution procedure makes the essential boundary conditions enforced directly. The results obtained by EFGM combining mass lumping technique are compared with those obtained by finite element method as well as analytical solutions, which shows that the solutions of the present method are in good agreement with FEM’s and analytical solutions. |
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