High-order methods and mesh adaptation for Euler equations
In this paper, we point out a novel contribution of mesh adaptation to high‐order methods for stationary and time‐dependent problems. From theoretical results, we exhibit that mesh adaptation, based on an adjoint‐free method, achieves a global second‐order mesh convergence for numerical solutions wi...
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| Published in: | International journal for numerical methods in fluids Vol. 56; no. 8; pp. 1069 - 1076 |
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| Format: | Journal Article Conference Proceeding |
| Language: | English |
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Chichester, UK
John Wiley & Sons, Ltd
20-03-2008
Wiley |
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| Abstract | In this paper, we point out a novel contribution of mesh adaptation to high‐order methods for stationary and time‐dependent problems. From theoretical results, we exhibit that mesh adaptation, based on an adjoint‐free method, achieves a global second‐order mesh convergence for numerical solutions with discontinuities in Lp norm. To attain this result, it is mandatory to combine together all mesh adaptive methods developed in the previous work. This theoretical result is validated on 2D and 3D examples for stationary and time‐dependent simulations. Copyright © 2008 John Wiley & Sons, Ltd. |
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| AbstractList | In this paper, we point out a novel contribution of mesh adaptation to high-order methods for stationary and time-dependent problems. From theoretical results, we exhibit that mesh adaptation, based on an adjoint-free method, achieves a global second-order mesh convergence for numerical solutions with discontinuities in Lp norm. To attain this result, it is mandatory to combine together all mesh adaptive methods developed in the previous work. This theoretical result is validated on 2D and 3D examples for stationary and time-dependent simulations. In this paper, we point out a novel contribution of mesh adaptation to high‐order methods for stationary and time‐dependent problems. From theoretical results, we exhibit that mesh adaptation, based on an adjoint‐free method, achieves a global second‐order mesh convergence for numerical solutions with discontinuities in L p norm. To attain this result, it is mandatory to combine together all mesh adaptive methods developed in the previous work. This theoretical result is validated on 2D and 3D examples for stationary and time‐dependent simulations. Copyright © 2008 John Wiley & Sons, Ltd. In this paper, we point out a novel contribution of mesh adaptation to high‐order methods for stationary and time‐dependent problems. From theoretical results, we exhibit that mesh adaptation, based on an adjoint‐free method, achieves a global second‐order mesh convergence for numerical solutions with discontinuities in Lp norm. To attain this result, it is mandatory to combine together all mesh adaptive methods developed in the previous work. This theoretical result is validated on 2D and 3D examples for stationary and time‐dependent simulations. Copyright © 2008 John Wiley & Sons, Ltd. |
| Author | Alauzet, F. |
| Author_xml | – sequence: 1 givenname: F. surname: Alauzet fullname: Alauzet, F. email: frederic.alauzet@inria.fr organization: INRIA-Gamma Project, Domaine de Voluceau, Le Chesnay 78153, France |
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| Cites_doi | 10.3166/remn.15.767-798 10.1016/j.jcp.2006.08.012 10.1137/0914082 10.1006/jcph.2001.6967 10.1007/978-3-540-34958-7_12 10.1016/0021-9991(78)90023-2 10.1016/S0045-7930(98)00059-0 |
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| Keywords | Three dimensional flow Computational fluid dynamics Anisotropy Digital simulation anisotropic mesh adaptation Modelling Euler equations Adaptive method Numerical convergence Mesh generation high-order method unstructured meshes |
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| References | Venditti D, Darmofal D. Grid adaptation for functional outputs: application to two-dimensional inviscid flows. Journal of Computational Physics 2002; 176(1):40-69. Giles MB, Pierce NA. In Adjoint Error Correction for Integral Outputs. Lecture Notes in Computational Science and Engineering, vol. 25, Barth T, Deconinck H (eds). Springer: Berlin, 2002; 47-96. Schulz-Rinne CW, Collins JP, Glaz HM. Numerical solution of the Riemann problem for two-dimensional gas dynamics. SIAM Journal on Scientific Computing 1993; 14(6):1394-1414. Sod GA. A survey of several finite difference methods for systems of nonlinear hyperbolic conservation laws. Journal of Computational Physics 1978; 27:1-31. Cournède P-H, Koobus B, Dervieux A. Positivity statements for a mixed-element-volume scheme on fixed and moving grids. European Journal of Computational Mechanics 2006; 15(7-8):767-798. Debiez C, Dervieux A. Mixed-element-volume MUSCL methods with weak viscosity for steady and unsteady flow calculations. Computers and Fluids 2000; 29:89-118. Alauzet F, Frey PJ, George P-L, Mohammadi B. 3D transient fixed point mesh adaptation for time-dependent problems: application to CFD simulations. Journal of Computational Physics 2007; 222:592-623. Frey PJ, George P-L. Mesh Generation. Application to Finite Elements. Hermès Science: Paris, Oxford, 2000. 1993; 14 2007; 222 2006 2000; 29 1978; 27 2002 2002; 176 2000 2006; 15 e_1_2_1_7_2 e_1_2_1_4_2 e_1_2_1_5_2 e_1_2_1_3_2 Giles MB (e_1_2_1_2_2) 2002 e_1_2_1_10_2 Frey PJ (e_1_2_1_6_2) 2000 e_1_2_1_8_2 e_1_2_1_9_2 |
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| Snippet | In this paper, we point out a novel contribution of mesh adaptation to high‐order methods for stationary and time‐dependent problems. From theoretical results,... In this paper, we point out a novel contribution of mesh adaptation to high-order methods for stationary and time-dependent problems. From theoretical results,... |
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| SubjectTerms | anisotropic mesh adaptation Computational methods in fluid dynamics Euler equations Exact sciences and technology Fluid dynamics Fundamental areas of phenomenology (including applications) high-order method Physics unstructured meshes |
| Title | High-order methods and mesh adaptation for Euler equations |
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