Lattice evolution solution for the nonlinear Poisson–Boltzmann equation in confined domains |
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| Institution: | 1. Department of Engineering Mechanics, Tsinghua University, Beijing 100084, China;2. Department of Mechanical Engineering, the Johns Hopkins University, Baltimore, MD 21218, USA;1. Department of Mechanical Engineering, Technical University of Denmark, Produktionstorvet, 2800 Kgs. Lyngby, Denmark;2. Department of Civil and Environmental Engineering, Princeton University, Princeton, NJ 08544, USA;1. School of Science, Southwest University of Science and Technology, Mianyang, Sichuan 610064, China;2. State Key Laboratory Cultivation Base for Nonmetal Composites and Functional Materials, Southwest University of Science and Technology, Mianyang, Sichuan 610064, China;3. Mineral Physics Institute, State University of New York at Stony Brook, New York 11794-2100, USA;4. Laboratory for Shock Wave and Detonation Physics Research, Institute of Fluid Physics, Chinese Academy of Engineering Physics, Mianyang 621900, China;1. Petroleum Exploration and Production Research Institute of SINOPEC, Beijing 100083, China;2. State Key Laboratory for Turbulence and Complex Systems and Department of Mechanics and Aerospace Engineering, College of Engineering, Peking University, Beijing 100871, China |
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| Abstract: | The lattice evolution method for solving the nonlinear Poisson–Boltzmann equation in confined domain is developed by introducing the second-order accurate Dirichlet and Neumann boundary implements, which are consistent with the non-slip model in lattice Boltzmann method for fluid flows. The lattice evolution method is validated by comparing with various analytical solutions and shows superior to the classical numerical solvers of the nonlinear Poisson equations with Neumann boundary conditions. The accuracy and stability of the method are discussed. This lattice evolution nonlinear Poisson–Boltzmann solver is suitable for efficient parallel computing, complex geometry conditions, and easy extension to three-dimensional cases. |
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