Rarefied gas flow in a triangular duct based on a boundary fitted lattice |
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| Institution: | 1. School of Mathematical Sciences, Peking University, Beijing, China;2. CAPT, LMAM & School of Mathematical Sciences, Peking University, Beijing, China;3. Department of Applied Mathematics, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong;1. Department of Mathematics & Statistics, Old Dominion University, Norfolk, VA 23529, USA;2. Computational Science Research Center, Beijing 10084, China;3. Fujian Provincial Key Laboratory on Mathematical Modeling & High Performance Scientific Computing and School of Mathematical Sciences, Xiamen University, Xiamen, China;4. Department of Mathematics, Purdue University, West Lafayette, IN 47907, USA;1. Department of Mathematics and Statistics, Al-Imam University, Riyadh, Saudi Arabia;2. Department of Mathematics and Statistical Sciences & Department of Mechanical, Energy and Industrial Engineering, Botswana International University of Science and Technology, Palapye, Botswana;3. Centro de Investigación en Creatividad y Educación Superior y Departamento de Ingeniería Mecánica, Universidad de Santiago de Chile, Santiago, Chile |
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| Abstract: | The rarefied fully developed flow of a gas through a duct of a triangular cross section is solved in the whole range of the Knudsen number. The flow is modelled by the BGK kinetic equation, subject to Maxwell diffuse boundary conditions. The numerical solution is based on the discrete velocity method, which is applied for first time on a triangular lattice in the physical space. The boundaries of the flow and computational domains are identical deducing accurate results with modest computational effort. Results on the velocity profiles and on the flow rates for ducts of various triangular cross sections are reported and they are valid in the whole range of gas rarefaction. Their accuracy is validated in several ways, including the recovery of the analytical solutions at the free molecular and hydrodynamic limits. The successful implementation of the triangular grid elements is promising for generalizing kinetic type solutions to rarefied flows in domains with complex boundaries using adaptive and unstructured grids. |
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