A nonlinear filtering algorithm for multi-dimensional finite element pollutant advection schemes |
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| Affiliation: | 1. Department of Aerodynamics, College of Aerospace Engineering, Nanjing University of Aeronautics and Astronautics, Yudao Street, Nanjing 210016, Jiangsu, China;2. Department of Mechanical Engineering, National University of Singapore, 10 Kent Ridge Crescent, Singapore 117576, Singapore;3. Temasek Laboratories, National University of Singapore, 5A Engineering Drive 1, Singapore 117411, Singapore;1. School of Logistics Engineering, Wuhan University of Technology, Wuhan 430070, China;2. Engineering Research Center of Port Logistics Technology and Equipment, Ministry of Education, Wuhan 430070, China;3. Beijing Computational Science Research Center, Haidian District, Beijing 100094, China;4. Research Institute of Tsinghua University in Shenzhen, Shenzhen 518057, China;5. ICORE GROUP INC, Shenzhen 518057, China;6. Department of Mathematics & Statistics, Old Dominion University, Norfolk, VA 23529, USA;7. Department of Computer Science, California State Polytechnic University, Pomona, USA;1. Department of Energy Resources Engineering, Stanford University, Stanford, CA 94305, United States of America;2. Department of Applied Mathematics and Statistics, UC Santa Cruz, Santa Cruz, CA 95064, United States of America;1. Department of Mechanical Engineering, National Institute of Technology, Durgapur, Durgapur 713209, India;2. Advanced Design and Analysis Group, CSIR-Central Mechanical Engineering Research Institute, Durgapur 713209, India;1. James Weir Fluids Laboratory, Department of Mechanical and Aerospace Engineering, University of Strathclyde, Glasgow G1 1XJ, UK;2. School of Engineering, University of Edinburgh, Edinburgh EH9 3FB, UK;3. School of Aeronautic Science and Engineering, Beihang University, Beijing 100191, China;4. School of Energy and Power Engineering, Xi''an Jiaotong University, 28 West Xianning Road, Xi''an 710049, China |
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| Abstract: | A nonlinear filter is developed for use with finite element methods in solving the atmospheric diffusion equation. Usually, high-order accurate finite element methods lead to ripples near sharp gradients. This is an undesirable feature in air quality modeling. The filter eliminates these ripples by adding artificial diffusion along the direction of the streamlines. Since it is applied only in regions where the ripples are located, the accuracy of the solution is maintained. Here, the filter was used with the streamline upwind Petrov-Galerkin method. It displayed good performance characteristics in the standard rotating puff test, and in a new test where the angular velocity profile is parabolic. It did not cause excessive crosswind diffusion that was present in a previously developed two-dimensional filter, or Forester filters applied to one-dimensional, spatially split algorithms. The new test problem was designed specifically to show that the rotating puff test may not always be the appropriate test to evaluate the performance of transport schemes, especially those that split the horizontal transport into one-dimensional operators. As expected, a one-dimensional splitting scheme (Chapeau function) displayed worse performance than fully two-dimensional schemes under more severe conditions of the new test problem. |
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