Error Estimation and Adaptive Mesh Refinement for Aerodynamic Flows

Hartmann, Ralf; Held, Joachim; Leicht, Tobias; Prill, Florian

doi:10.1007/978-3-642-03707-8_24

Cited by 35 publications

(38 citation statements)

References 66 publications

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“…These tolerances have been specified within the European Union project ADIGMA as representative of industrial requirements [41]. Fig.…”

Section: Numerical Resultsmentioning

confidence: 99%

“…Figure 11 shows the C D coefficient computed at each adaptation cycle for the three methodologies and compared against the uniform refinement and Richardson extrapolation results. Note that, in this case, the adjoint C D tolerance was lowered to 0.0001 because the initial mesh already yields a drag value clearly below industrial tolerance [41]. Assuming that the correct value is obtained by uniform refinement, the featured based method gives a totally wrong result.…”

Section: High Transonic Flow Conditionsmentioning

confidence: 99%

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Comparison of Mesh Adaptation Using the Adjoint Methodology and Truncation Error Estimates

2012

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Mesh adaptation based on error estimation has become a key technique to improve the accuracy of computationalfluid-dynamics computations. The adjoint-based approach for error estimation is one of the most promising techniques for computational-fluid-dynamics applications. Nevertheless, the level of implementation of this technique in the aeronautical industrial environment is still low because it is a computationally expensive method. In the present investigation, a new mesh refinement method based on estimation of truncation error is presented in the context of finite-volume discretization. The T estimation method uses auxiliary coarser meshes to estimate the local truncation error, which can be used for driving an adaptation algorithm. The method is demonstrated in the context of two-dimensional NACA0012 and three-dimensional ONERA M6 wing inviscid flows, and the results are compared against the adjoint-based approach and physical sensors based on features of the flow field.

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“…These tolerances have been specified within the European Union project ADIGMA as representative of industrial requirements [41]. Fig.…”

Section: Numerical Resultsmentioning

confidence: 99%

Section: High Transonic Flow Conditionsmentioning

confidence: 99%

Comparison of Mesh Adaptation Using the Adjoint Methodology and Truncation Error Estimates

2012

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“…This is, in a sense, qualitatively similar in character to the adjoint solutions computed for first-order hyperbolic conservation laws, when the functional of interest is a point evaluation of the primal solution, cf. [30,32], for example. However, in this setting, we do observe some growth in the height of the δ´type adjoint solution along the path of interest, as we move from the release point to the boundary of the computational domain Ω.…”

Section: Numerical Experimentsmentioning

confidence: 99%

“…Goal-oriented a posteriori error estimation seeks to determine whether some physical quantity of interest, calculated using the numerical solution, is within a given tolerance of the true value. Goal-oriented techniques for a posteriori error estimation were introduced in [6,25]; see also [7,8,26,29,30,31,32,33,34,38,39,45], and the references cited therein. The formulation in [6] constructs an adjoint-weighted error bound, whilst the alternative formulation in [25] constructs an unweighted error bound based on exploiting stability estimates.…”

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confidence: 99%

Goal-Oriented A Posteriori Error Estimation For The Travel Time Functional In Porous Media Flows

Cliffe¹,

Collis²,

Houston³

2015

SIAM J. Sci. Comput.

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Abstract. In this article we consider the a posteriori error estimation and adaptive mesh refinement for the numerical approximation of the travel time functional arising in porous media flows. The key application of this work is in the safety assessment of radioactive waste facilities; in this setting, the travel time functional measures the time taken for a non-sorbing radioactive solute, transported by groundwater, to travel from a potential site deep underground to the biosphere. To ensure the computability of the travel time functional, we employ a mixed formulation of Darcy's law and conservation of mass, together with Raviart-Thomas Hpdiv, Ωq-conforming finite elements. The proposed a posteriori error bound is derived based on a variant of the standard Dual-WeightedResidual approximation, which takes into account the lack of smoothness of the underlying functional of interest. The proposed adaptive refinement strategy is tested on both a simple academic test case and a problem based on the geological units found at the Sellafield site in the UK.Key words. Travel time functional, groundwater flows, adaptivity, goal-oriented a posteriori error estimation, mixed finite element methods 1. Introduction. In recent decades the use of numerical simulations in hydrogeological studies has become commonplace across a range of applications. Amongst these, modelling the post-closure safety performance of deep geological storage of radioactive waste is of particular interest for a posteriori error estimation. Efficient and reliable simulations are required in order to assess the suitability of a specific location for siting a waste repository. Furthermore, there is a critical need to verify any computational results with rigorous error bounds as the effects of an inaccurate simulation could be extremely costly. In the safety assessment of radioactive waste facilities, one of the key quantities of interest is the time taken for a non-sorbing radioactive solute, transported by groundwater, to travel from a potential site deep underground to the biosphere [28,41,44]. Additionally, accurate computation of the travel time has applications in streamline methods for modelling other subsurface flows; for instance in oil and gas reservoir management [36].The suitability of finite element methods has been demonstrated for many of the complex geometries and physical effects that are associated with the numerical approximation of groundwater flow and contaminant transport problems [16,17,20,21,37,41,42]. There are, however, problems associated with the use of nodal-based elements, such as lack of mass conservation at an elemental level and unphysical streamlines, as noted in [21,24,42,43]. These problems are not observed when using a (conforming) mixed finite element method, or finite difference method, in which pressure and velocity are computed simultaneously. Indeed, when employing the latter class of methods on triangular meshes, the tracing of streamlines is straightforward and has been shown to yield physical results, even o...

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“…Some of the main reasons for this increase of interest in DG methods is that allowing for discontinuities across elements gives extraordinary flexibility in terms of mesh design and choice of shape functions. Additionally, hp-DG, which are based on locally refined meshes and variable approximation orders, have been shown to achieve tremendous gains in computational efficiency for challenging problems [6,7,8,9,10,1,11,12,13].…”

Section: Discrete Eigenvalue Problemsmentioning

confidence: 99%

A hp-adaptive discontinuous Galerkin method for plasmonic waveguides

Giani¹

2014

Journal of Computational and Applied Mathematics

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Publisher's copyright statement: NOTICE: this is the author's version of a work that was accepted for publication in Journal of Computational and Applied Mathematics. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reected in this document. Changes may have been made to this work since it was submitted for publication. A denitive version was subsequently published in Journal of Computational and Applied Mathematics, 270, November 2014, 10.1016/j.cam.2014.009. Use policyThe full-text may be used and/or reproduced, and given to third parties in any format or medium, without prior permission or charge, for personal research or study, educational, or not-for-prot purposes provided that:• a full bibliographic reference is made to the original source • a link is made to the metadata record in DRO • the full-text is not changed in any way The full-text must not be sold in any format or medium without the formal permission of the copyright holders.Please consult the full DRO policy for further details. AbstractIn this paper we propose and analyse a hp-adaptive discontinuous finite element method for computing electromagnetic modes of propagation supported by waveguide structures comprised of a thin lossy metal film of finite width embedded in an infinite homogeneous dielectric. We propose a goal-oriented or dual weighted residual error estimator based on the solution of a dual problem that we use to drive the adaptive refinement with the aim to compute accurate approximation of the modes. We illustrate in the last section the benefits of the resulting hp-adaptive method in practice, which consist in fast convergence and accurate estimation of the error. We tested the method computing the vanishing modes for a metallic waveguide of square section.

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Error Estimation and Adaptive Mesh Refinement for Aerodynamic Flows

Cited by 35 publications

References 66 publications

Comparison of Mesh Adaptation Using the Adjoint Methodology and Truncation Error Estimates

Comparison of Mesh Adaptation Using the Adjoint Methodology and Truncation Error Estimates

Goal-Oriented A Posteriori Error Estimation For The Travel Time Functional In Porous Media Flows

A hp-adaptive discontinuous Galerkin method for plasmonic waveguides

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