On the simulation of wave propagation with a higher-order finite volume scheme based on Reproducing Kernel Methods |
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| Authors: | X Nogueira I Colominas L Cueto-Felgueroso S Khelladi |
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| Affiliation: | 1. Group of Numerical Methods in Engineering, Dept. of Applied Mathematics, Universidade da Coruña, Campus de Elviña, 15071 A Coruña, Spain;2. Dept. of Civil and Environmental Engineering, Massachusetts Institute of Technology, 77 Massachusetts Ave., Cambridge, MA 02139, USA;3. Arts et Métiers ParisTech, 151 boulevard de l’Hôpital, 75013 Paris, France;1. Seminar for Applied Mathematics, ETH, HG, G. 57.1, Rämistrasse 101, Zürich, Switzerland;2. Seminar for Applied Mathematics, ETH, HG G. 57.2, Rämistrasse 101, Zürich, Switzerland;3. Computational Science and Engineering Laboratory, ETH, CLT E 13, Clausiusstrasse 33, Zürich, Switzerland;1. Department of Aerospace and Ocean Engineering, Virginia Tech, 215 Randolph Hall, 460 Old Turner Street, Blacksburg, VA 24061, USA;2. Department of Mechanical Engineering, The University of British Columbia, 2054-6250 Applied Science Lane, Vancouver, B.C., V6T 1Z4, Canada;1. CFD Team, CERFACS, 42 avenue Gaspard Coriolis, 31057 Toulouse, France;2. Department of Mechanical Engineering, University of Sherbrooke, Sherbrooke, J1K 2R1, QC, Canada |
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| Abstract: | In this work we study the dispersion and dissipation characteristics of a higher-order finite volume method based on Moving Least Squares approximations (FV-MLS), and we analyze the influence of the kernel parameters on the properties of the scheme. Several numerical examples are included. The results clearly show a significant improvement of dispersion and dissipation properties of the numerical method if the third-order FV-MLS scheme is used compared with the second-order one. Moreover, with the explicit fourth-order Runge–Kutta scheme the dispersion error is lower than with the third-order Runge–Kutta scheme, whereas the dissipation error is similar for both time-integration schemes. It is also shown than a CFL number lower than 0.8 is required to avoid an unacceptable dispersion error. |
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