Some techniques for improving the resolution of finite difference component-wise WENO schemes for polydisperse sedimentation models |
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| Affiliation: | 1. Harbin Institute of Technology, Shenzhen Graduate School, Shenzhen, 518055, PR China;2. College of Mathematics and Statistics, Northeastern University at Qinhuangdao, Qinhuangdao, 066004, PR China;3. Department of Mathematics, Harbin Institute of Technology, Harbin, 150001, PR China;1. J. Heyrovský Institute of Physical Chemistry, Academy of Sciences of the Czech Republic, Dolejškova 3, 182 23 Prague 8, Czech Republic;2. Department of Physical and Macromolecular Chemistry, Faculty of Science, Charles University, Albertov 2030, 128 40 Prague 2, Czech Republic;1. Department of Computational and Applied Mathematics, China University of Petroleum, Qingdao 266580, PR China;2. Department of Mathematics, East China Normal University, Shanghai 200062, PR China;3. Laboratório Nacional de Computação Científica, MCTI Avenida Getúlio Vargas 333, 25651-075 Petrópolis, RJ, Brazil;1. Department of Physics, University College of Engineering, Panruti, India;2. Department of Physics, SRM University, Ramapuram Campus, Chennai, India;3. Department of Optoelectronics, University of Kerala, Kariavattom, Kerala 695581, India;1. Laboratory of Computational Physics, Institute of Applied Physics and Computational Mathematics, Beijing, China;2. Center for Applied Physics and Technology, Peking University, Beijing, China |
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| Abstract: | Polydisperse sedimentation models can be described by a system of conservation laws for the concentration of each species of solids. Some of these models, as the Masliyah–Locket–Bassoon model, can be proven to be hyperbolic, but its full characteristic structure cannot be computed in closed form. Component-wise finite difference WENO schemes may be used in these cases, but these schemes suffer from an excessive diffusion and may present spurious oscillations near shocks. In this work we propose to use a flux-splitting that prescribes less numerical viscosity for component-wise finite difference WENO schemes. We compare this technique with others to alleviate the diffusion and oscillatory behavior of the solutions obtained with component-wise finite difference WENO methods. |
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| Keywords: | Finite difference WENO schemes Component-wise schemes HLL flux-splitting Polydisperse sedimentation |
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