The reservoir technique: a way to make Godunov-type schemes zero or very low diffuse. Application to Colella–Glaz solver |
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| Institution: | 1. Laboratoire de Mathématiques, Université d''Orsay, 91405 Orsay, France;2. Laboratoire MAS, Ecole Centrale de Paris, Grande voie des vignes, 92295 Chatenay-Malabry, France;3. Centre de Mathématiques et de Leurs Applications, ENS de Cachan, 61, avenue du président Wilson, 94235 Cachan cedex, France;4. Centre de Recherches Mathématiques, Université de Montréal, 2920 Chemin de la Tour, H3T 1J4, Canada;5. University of Ontario Institute of Technology, 2000 Simcoe Street North, L1H 7Y4, Oshawa, Canada;1. Departament de Matemàtica Aplicada III, Universitat Politècnica de Catalunya, Mod. C2, Campus Nord, C/Jordi Girona Salgado 1-3, 08034 Barcelona, Spain;2. Departament de Matemàtica Aplicada I, Universitat Politècnica de Catalunya, Av. Gregorio Marañón 44-50, 08028 Barcelona, Spain;1. Department of Banking and Finance, Faculty of Economics, University of Zurich, Switzerland;2. Institute of Computational Science, Università della Svizzera italiana, Via Giuseppe Buffi 13, CH-6900 Lugano, Switzerland;1. Department of Mechanical Engineering, Carnegie Mellon University, 5000 Forbes Avenue, Pittsburgh, PA 15213, USA;2. Department of Mechanical Engineering, Pohang University of Science and Technology, 77 Cheongam-ro, Nam-gu, Pohang, Gyeongbuk 37673, Republic of Korea;1. Computing & Mathematical Sciences, California Institute of Technology, United States;2. Department of Mathematics, Simon Fraser University, Canada |
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| Abstract: | Although it is commonly thought that first order schemes are not accurate enough to approximate nonlinear hyperbolic problems, we here explore a conservative time integration with global time steps but local updates (see F. Alouges, F. De Vuyst, G. Le Coq, E. Lorin, Un procédé de réduction de la diffusion numérique des schémas à différence de flux d'ordre un pour les systèmes hyperboliques non linéaires, C. R. Math. Acad. Sci. Paris, Ser. I 335 (7) (2002) 627–632. 1]]; F. Alouges, F. De Vuyst, G. Le Coq, E. Lorin, The reservoir scheme for systems of conservation laws, in: Finite Volumes for Complex Applications, III, Porquerolles, 2002, Lab. Anal. Topol. Probab. CNRS, Marseille, 2002, pp. 247–254 (electronic). 2]]). This overall conservative method can be interpreted as a system of reservoirs at cell interfaces that fill up and empty when local CFL conditions are reached. For Euler equations, particularly good results are obtained when one uses this technique together with the Riemann solver proposed by Colella and Glaz. |
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