## Grid adaptation for functional outputs: application to two-dimensional inviscid flows

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Venue: | J. Comput. Phys |

Citations: | 65 - 17 self |

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@ARTICLE{Venditti_gridadaptation,

author = {David A. Venditti and David L. Darmofal},

title = {Grid adaptation for functional outputs: application to two-dimensional inviscid flows},

journal = {J. Comput. Phys},

year = {},

pages = {40--69}

}

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www.elsevier.com/locate/jcp

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Citation Context ...y ill-conditioned on highly stretched elements resulting in numerical instabilities. To circumvent this issue, the least squares problem is solved using a singular value decomposition (SVD) algorithm =-=[49]-=-. The quadratic prolongation operator is used for evaluating the correction term in (10), and for computing the adaptive parameters described in Section 3.2. ð9Þs28 D.A. Venditti, D.L. Darmofal / Jour... |

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Citation Context ...me of research into a posteriori error analysis and optimal grid adaptation for functional outputs within the context of finite element methods for fluid dynamics. Becker, Rannacher and collaborators =-=[8,9,11,42]-=- have developed an optimal control approach for output-based grid adaptation within a Galerkin finite element framework. Patera, Peraire and collaborators [29,37,38] have established an implicit a pos... |

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Citation Context ...sics 187 (2003) 22–46 23 in the estimation of drag during a recent CFD drag prediction workshop [27]. While automatic grid adaptation has shown significant potential for improving the accuracy of CFD =-=[1,7,12,13,22,30, 39,41,53,54,56]-=-, to date these methods have not been able to demonstrate reliable improvements in the solution accuracy. A major difficulty in achieving definite improvements using current adaptive methods for Euler... |

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Citation Context ... have established an implicit a posteriori procedure for computing upper and lower bounds on functional outputs of finite element solutions. Other researchers in the area include S€uli and co-workers =-=[18,24,47]-=-, Larson and Barth [25], and Formaggia et al. [16]. For general discretizations, Pierce and Giles [19–21,40] have developed an adjoint-based error correction technique for functional outputs that exte... |

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Citation Context ...sics 187 (2003) 22–46 23 in the estimation of drag during a recent CFD drag prediction workshop [27]. While automatic grid adaptation has shown significant potential for improving the accuracy of CFD =-=[1,7,12,13,22,30, 39,41,53,54,56]-=-, to date these methods have not been able to demonstrate reliable improvements in the solution accuracy. A major difficulty in achieving definite improvements using current adaptive methods for Euler... |

39 | Adjoint error estimation and grid adaptation for funcional outputs: Application to quasi-one-dimensional flow - Venditti, Darmofal |

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Citation Context ...cker, Rannacher and collaborators [8,9,11,42] have developed an optimal control approach for output-based grid adaptation within a Galerkin finite element framework. Patera, Peraire and collaborators =-=[29,37,38]-=- have established an implicit a posteriori procedure for computing upper and lower bounds on functional outputs of finite element solutions. Other researchers in the area include S€uli and co-workers ... |

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Citation Context ...sics 187 (2003) 22–46 23 in the estimation of drag during a recent CFD drag prediction workshop [27]. While automatic grid adaptation has shown significant potential for improving the accuracy of CFD =-=[1,7,12,13,22,30, 39,41,53,54,56]-=-, to date these methods have not been able to demonstrate reliable improvements in the solution accuracy. A major difficulty in achieving definite improvements using current adaptive methods for Euler... |

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Citation Context ...appropriate constant on the right-hand-side of (32) is dependent on the standard employed by the particular grid generator. In BL2D and BAMG, physical lengths are mapped onto a metric length of unity =-=[23,26]-=-.D.A. Venditti, D.L. Darmofal / Journal of Computational Physics 187 (2003) 22–46 35 Fig. 3. Typical triangle in the current grid. This results in the system of equations ðDx1Þ 2 2Dx1Dy1 ðDy1Þ 2 ðDx2... |

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Citation Context ...ined from other sources such as an asymptotic expansion, a reduced order model, or an entirely different discretization. The impetus for this procedure is the correction technique of Pierce and Giles =-=[21,40]-=-. Let dUh represent a small perturbation in the primal solution. Each component of the vector dUh corresponds to the local error in the perturbed solution relative to the exact solution of the primal ... |

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Citation Context ...rrespondingly, the discrete adjoint takes on a different character on the boundary relative to the interior. This behavior has been observed previously [6]. Mathematical illustrations are provided in =-=[17,50]-=-. Fig. 1 shows contour distributions (middle and right plots) of the discrete adjoint x-momentum variable for a simulation of laminar flow past a cylinder. The corresponding grid is plotted on the lef... |

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