Application of the Chebyshev pseudospectral method to van der Waals fluids |
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| Authors: | Tinuade Odeyemi Abdolmajid Mohammadian Ousmane Seidou |
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| Institution: | 1. Laboratoire Interdisciplinaire Carnot de Bourgogne (ICB), UMR 6303 CNRS - Université Bourgogne Franche-Comté, F-21078 Dijon, France;2. Laboratoire de Probabilités et Modèles Aléatoires, University Paris Diderot, 75205 Paris Cedex 13, France;3. School of Engineering and Physical Sciences, SUPA, Heriot–Watt University, Edinburgh EH14 4AS, UK;4. Department of Engineering, University of Ferrara, Via Saragat 1, 44122 Ferrara, Italy;1. School of Mathematical Sciences, University of Science and Technology of China, Hefei, Anhui 230026, PR China;2. Department of Mathematics, City University of Hong Kong, 83 Tat Chee Avenue, Kowloon Tong, Hong Kong |
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| Abstract: | In this paper, we consider a class of van der Waals flows with non-convex flux functions. In these flows, nonclassical under-compressive shock waves can develop. Such waves, which are characterized by kinetic functions, violate classical entropy conditions. We propose to use a Chebyshev pseudospectral method for solving the governing equations. A comparison of the results of this method with very high-order (up to 10th-order accurate) finite difference schemes is presented, which shows that the proposed method leads to a lower level of numerical oscillations than other high-order finite difference schemes and also does not exhibit fast-traveling packages of short waves which are usually observed in high-order finite difference methods. The proposed method can thus successfully capture various complex regimes of waves and phase transitions in both elliptic and hyperbolic regimes. |
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