A lattice BGK model for advection and anisotropic dispersion equation |
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| Institution: | 1. Soil-Plant Dynamic Unit, Scottish Crop Research Institute, Dundee DD2 5DA, UK;2. SIMBIOS Center, University of Abertay Dundee, Bell Street, Dundee DD1 9GH, UK;1. Key Laboratory on Deep GeoDrilling Technology of the Ministry of Land and Resources, School of Engineering and Technology, China University of Geosciences, Beijing 100083, PR China;2. State Key Laboratory of New Ceramics and Fine Processing, Tsinghua University, Beijing 100084, PR China;1. Emergency Medical Centre of the Osje?ko-Baranjska County, Josipa Hutllera 2, 31000 Osijek, Croatia;2. Chief of the Department for Traumatology and Orthopaedics, University Hospital Dubrava, Zagreb, Av. Gojka Suska 6, HR-10040 Zagreb, Croatia;1. Czech Technical University in Prague, Faculty of Nuclear Sciences and Physical Engineering, B?ehová 7, 115 19 Prague 1, Czech Republic;2. Retired Fellow, Los Alamos National Laboratory, Los Alamos, NM, USA |
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| Abstract: | This paper presents a lattice Boltzmann model (LBM) for 2-D advection and anisotropic dispersion equation (AADE) based on the Bhatnagar, Gross and Krook (BGK) model. In the proposed model, the particle speed space is discretized using a rectangular lattice that has four speeds in nine directions, and the single relaxation time is assumed to be directionally dependent. To ensure that the collision is mass-invariant when the relaxation time is directionally dependent, the concentration is calculated from a weighted summation of the particle distribution functions. The proposed model was verified against benchmark problems and the finite difference solution of solute transport with spatially variable dispersion coefficients and non-uniform velocity field. The significant results are that it conserves mass perfectly and offers accurate and efficient solutions for both dispersion-dominated and advection-dominated problems. |
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