Hybrid Flux-Splitting Schemes for a Two-Phase Flow Model |
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| Institution: | 1. Japan Atomic Energy Agency, Tokai-mura, Naka-gun, Ibaraki 319-1195, Japan;2. College of Industrial Technology, Nihon University, Narashino, Chiba 275-8575, Japan;1. Department of Electrical and Computer Engineering, McGill University, Montreal, QC H3A0E9, Canada;2. Department of Mathematical Sciences, NJIT, Newark, NJ 07102-1982, USA;3. Department of Mathematics and Statistics, McGill University, Montreal, QC H3A0B9, Canada;1. Thermal & Fluid System R&D Group, Korea Institute of Industrial Technology, 89 Yangdaegiro-gil, Ipjang-myeon, Seobuk-gu, Cheonan, 331-822, Republic of Korea;2. Department of Mechanical Engineering, Yonsei University, 50 Yonsei-ro, Seodaemun-gu, Seoul, 120-749, Republic of Korea;3. Energy System Engineering, University of Science and Technology, 217 Gajeong-ro, Yuseong-gu, Daejeon, Republic of Korea;1. State Key Laboratory of Petroleum Resources and Prospecting, China University of Petroleum, Beijing 102249, China;2. China National Oil and Gas Exploration and Development Company Ltd, Beijing 100034, China;1. Key Laboratory of Energy Thermal Conversion and Control of Ministry of Education, School of Energy and Environment, Southeast University, Nanjing, Jiangsu 210096, China;2. Heat and Mass Transfer Technological Center, Technical University of Catalonia, Terrassa, Barcelona 08222, Spain;3. School of Mathematics and Computational Science, Xiangtan University, Hunan 411105, China;4. Department of Chemical Engineering, Monash University, Clayton, Vic 3800, Australia;5. School of Mechanical Engineering, Xiangtan University, Hunan 411105, China |
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| Abstract: | In this paper we deal with the construction of hybrid flux-vector-splitting (FVS) schemes and flux-difference-splitting (FDS) schemes for a two-phase model for one-dimensional flow. The model consists of two mass conservation equations (one for each phase) and a common momentum equation. The complexity of this model, as far as numerical computation is concerned, is related to the fact that the flux cannot be expressed in terms of its conservative variables. This is the motivation for studying numerical schemes which are not based on (approximate) Riemann solvers and/or calculations of Jacobian matrix. This work concerns the extension of an FVS type scheme, a Van Leer type scheme, and an advection upstream splitting method (AUSM) type scheme to the current two-phase model. Our schemes are obtained through natural extensions of corresponding schemes studied by Y. Wada and M.-S. Liou (1997, SIAM J. Sci. Comput.18, 633–657) for Euler equations. We explore the various schemes for flow cases which involve both fast and slow transients. In particular, we demonstrate that the FVS scheme is able to capture fast-propagating acoustic waves in a monotone way, while it introduces an excessive numerical dissipation at volume fraction contact (steady and moving) discontinuities. On the other hand, the AUSM scheme gives accurate resolution of contact discontinuities but produces oscillatory approximations of acoustic waves. This motivates us to propose other hybrid FVS/FDS schemes obtained by removing numerical dissipation at contact discontinuities in the FVS and Van Leer schemes. |
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