Investigation of Galilean invariance of multi-phase lattice Boltzmann methods |
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| Institution: | 1. Center for Combustion Energy, Key laboratory for Thermal Science and Power Engineering of Ministry of Education, Department of Energy and Power Engineering, Tsinghua University, Beijing 100084, China;2. Department of Mechanical Engineering, University College London, Torrington Place, London WC1E 7JE, UK;3. School of Energy Science and Engineering, Central South University, Changsha 410083, China;1. School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan 430074, China;2. State Key Laboratory of Coal Combustion, Huazhong University of Science and Technology, Wuhan 430074, China;3. School of Mathematics and Computational Science, Hunan First Normal University, Changsha 410205, China;1. Key Laboratory of Thermo-Fluid Science and Engineering of MOE, School of Energy and Power Engineering, Xi’an Jiaotong University, Xi’an, Shaanxi 710049, China;2. Computational Earth Science Group (EES-16), Los Alamos National Laboratory, Los Alamos, NM, USA;1. Key Laboratory of Low-grade Energy Utilization Technologies and Systems of Ministry of Education, Chongqing 400030, PR China;2. Key Laboratory of Renewable Energy and Gas Hydrate, Chinese Academy of Science, Guangzhou 510640, PR China;1. SINOPEC Petroleum Exploration and Production Research Institute, Beijing, PR China;2. State Key Laboratory of Petroleum Resources and Engineering in China University of Petroleum, Beijing, PR China;3. Ministry of Education Key Laboratory of Petroleum Engineering in China University of Petroleum, Beijing, PR China |
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| Abstract: | We examine the Galilean invariance of standard lattice Boltzmann methods for two-phase fluids. We show that the known Galilean invariant term that is cubic in the velocities, and is usually neglected, is a major source of Galilean invariance violations. We show that incorporating a correction term can improve the Galilean invariance of the method by up to two orders of magnitude for large velocities. We found that this is true in particular for methods in which the interactions are incorporated through a forcing term. Methods in which interactions are incorporated through a non-ideal pressure tensor only benefit for large velocities. |
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