A mixed Lagrangian–Eulerian method for non-linear free surface flows using multigrid on hierarchical Cartesian grids
This article describes a two-dimensional finite difference method for the numerical simulation of fully non-linear irrotational water waves. The computational domain is discretised in an Eulerian fashion using hierarchical Cartesian meshes, whilst the free surface location is explicitly tracked usin...
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| Veröffentlicht in: | Computers & fluids Jg. 36; H. 5; S. 914 - 923 |
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01.06.2007
Elsevier Science |
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| Abstract | This article describes a two-dimensional finite difference method for the numerical simulation of fully non-linear irrotational water waves. The computational domain is discretised in an Eulerian fashion using hierarchical Cartesian meshes, whilst the free surface location is explicitly tracked using a Lagrangian approach. The accuracy of the method is strongly dependent on the quality of the approximation to the free surface velocities and a novel method to compute these is proposed. A multigrid strategy is implemented to take advantage of the hierarchical nature of the grids, incorporating an efficient technique to generate the coarser grids. The method is verified through simulations of quasi-linear low-amplitude waves and through a comparative study using an asymmetric sloshing wave. The non-linear behaviour of waves of moderate amplitude is also simulated. |
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| AbstractList | This article describes a two-dimensional finite difference method for the numerical simulation of fully non-linear irrotational water waves. The computational domain is discretised in an Eulerian fashion using hierarchical Cartesian meshes, whilst the free surface location is explicitly tracked using a Lagrangian approach. The accuracy of the method is strongly dependent on the quality of the approximation to the free surface velocities and a novel method to compute these is proposed. A multigrid strategy is implemented to take advantage of the hierarchical nature of the grids, incorporating an efficient technique to generate the coarser grids. The method is verified through simulations of quasi-linear low-amplitude waves and through a comparative study using an asymmetric sloshing wave. The non-linear behaviour of waves of moderate amplitude is also simulated. |
| Author | Greaves, Deborah M. Silva Santos, Carlos M.P. |
| Author_xml | – sequence: 1 givenname: Carlos M.P. surname: Silva Santos fullname: Silva Santos, Carlos M.P. organization: CEsA Centro de Estudos de Energia Eólica e Escoamentos Atmosféricos, Faculdade de Engenharia da Universidade do Porto, Rua Dr. Roberto Frias, s/n, 4200-465 Porto, Portugal – sequence: 2 givenname: Deborah M. surname: Greaves fullname: Greaves, Deborah M. email: d.m.greaves@bath.ac.uk organization: Department of Architecture and Civil Engineering, University of Bath, Bath BA2 7AY, United Kingdom |
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| Cites_doi | 10.1007/978-94-011-3694-5_21 10.1016/0146-664X(82)90098-3 10.1007/978-94-010-9204-3_127 10.1016/0021-9991(88)90002-2 10.1115/1.2910291 10.1016/S0045-7930(96)00029-1 10.1016/0141-1187(94)00029-8 10.1016/0021-9991(92)90307-K 10.1016/0021-9991(81)90145-5 10.1002/1097-0363(20000830)33:8<1121::AID-FLD45>3.0.CO;2-H 10.5957/jsr.1997.41.3.181 10.1016/0021-9991(86)90011-2 10.1016/0141-1187(94)90028-0 |
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| Keywords | Euler Lagrange equation Wave propagation Multigrid Digital simulation Free surface flow Modelling Mesh generation Hierarchized structure Liquid sloshing Cartesian coordinates Finite difference method Non linear wave |
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| Title | A mixed Lagrangian–Eulerian method for non-linear free surface flows using multigrid on hierarchical Cartesian grids |
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