Verified predictions of shape sensitivities in wall-bounded turbulent flows by an adaptive finite-element method

Hay, Alexander; Pelletier, Dominique; Caro, Richard Di

doi:10.1016/j.jcp.2009.03.022

Cited by 5 publications

(5 citation statements)

References 49 publications

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“…The residual‐based strategy, such as the R‐parameter proposed by Ganesh et al ., can be used to devise a suitable criterion. Also, the sensitivity approach can be used to control the adaption process . An interesting review of various approaches has been given by Hay and Visonneau , and the most widely used methodologies are categorized into four kinds: Local error indicators. A posteriori error estimators. Residual‐based error indicators. Multiscale‐based techniques.…”

Section: Amr With Multi‐block Structured Curvilinear Meshmentioning

confidence: 99%

Accurate and robust adaptive mesh refinement for aerodynamic simulation with multi‐block structured curvilinear mesh

Chen

2015

Numerical Methods in Fluids

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SUMMARYA multi-block curvilinear mesh-based adaptive mesh refinement (AMR) method is developed to satisfy the competing objectives of improving accuracy and reducing cost. Body-fitted curvilinear mesh-based AMR is used to capture flow details of various length scales. A series of efforts are made to guarantee the accuracy and robustness of the AMR system. A physics-based refinement function is proposed, which is proved to be able to detect both shock wave and vortical flow. The curvilinear mesh is refined with cubic interpolation, which guarantees the aspect ratio and smoothness. Furthermore, to enable its application in complex configurations, a sub-block-based refinement strategy is developed to avoid generating invalid mesh, which is the consequence of non-smooth mesh lines or singular geometry features. A newfound problem of smaller wall distance, which negatively affects the stability and is never reported in the literature, is also discussed in detail, and an improved strategy is proposed. Together with the high-accuracy numerical scheme, a multiblock curvilinear mesh-based AMR system is developed. With a series of test cases, the current method is verified to be accurate and robust and be able to automatically capture the flow details at great cost saving compared with the global refinement.

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Section: Amr With Multi‐block Structured Curvilinear Meshmentioning

confidence: 99%

Accurate and robust adaptive mesh refinement for aerodynamic simulation with multi‐block structured curvilinear mesh

Chen

2015

Numerical Methods in Fluids

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“…Several recipes are available in the literature with the aim of improving the effectiveness of the recovery procedure (see, e.g., [29][30][31][32]). Although the theoretical properties of these recovery procedures are not yet very well understood [31,[33][34][35][36], recovery-based error estimators show an astonishing numerical robustness, heuristically assessed on different problem settings (see, e.g., [32,[37][38][39]). The main advantage of these estimators is the computational cheapness as well as the easiness of implementation: they do not involve any other quantity except for the solution and the corresponding gradient.…”

Section: An Anisotropic Recovery-based Error Estimatormentioning

confidence: 99%

Anisotropic mesh adaptation driven by a recovery‐based error estimator for shallow water flow modeling

Porta

Perotto

Ballio

2011

Numerical Methods in Fluids

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SUMMARY The aim of this paper is to propose an effective anisotropic mesh adaptation procedure for the solution of the shallow water equations. The hyperbolic partial differential equation system is solved via the streamline diffusion FEM, suitably modified by a shock‐capturing correction. The proposed adaptation procedure relies on a recovery‐based error estimator. In particular, we look for an anisotropic error estimator able to select not only the size but also the shape and the orientation of the mesh elements, with the aim of optimizing the computational advantages yielded by a standard isotropic mesh adaptation strategy. The robustness of the proposed estimator is assessed when either a single physical quantity, meaningful for the problem at hand, or a combination of all the shallow water system components drives the adaptation procedure. For this purpose, steady shallow water problems as well as unsteady configurations are considered. Copyright © 2011 John Wiley & Sons, Ltd.

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“…There is a wealth of publication on sensitivity analysis that presents the different methodologies to numerically compute shape sensitivities and the interested reader is referred to [13,20] for a broader discussion. We succinctly present here the most popular approaches to compute flow sensitivities:…”

Section: Formulation For the Direct Numerical Simulationmentioning

confidence: 99%

“…Consequently, the SEMs always compute a flow sensitivity for a fraction of the cost of computing the flow making these methodologies very attractive. The differences between SEMs depend on the order of the three operations: mapping, differentiation and discretization [20]. In the continuous sensitivity equation (CSE) approach, the governing equations are first differentiated and then discretized, whereas in the discrete sensitivity equation (DSE) approach, discretization is performed prior to differentiation.…”

Section: Formulation For the Direct Numerical Simulationmentioning

confidence: 99%

“…[27][28][29]). However, the CSE method offers a number of advantages over discrete sensitivity algorithms that have been extensively discussed in the literature [30,20]. Among them, we adopt the CSE method here for the two following reasons : First, in the case of shape parameters, the CSE method avoids the delicate issue of evaluating mesh sensitivities.…”

Section: Formulation For the Direct Numerical Simulationmentioning

confidence: 99%

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Reduced-order models for parameter dependent geometries based on shape sensitivity analysis

Hay

Borggaard

Akhtar

et al. 2010

Journal of Computational Physics

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Reduced-order models for parameter dependent geometries based on shape sensitivity analysis Hay, A.; Borggaard, J.; Akhtar, I.; Pelletier, D.Contact us / Contactez nous: nparc.cisti@nrc-cnrc.gc.ca. The proper orthogonal decomposition (POD) is widely used to derive low-dimensional models of large and complex systems. One of the main drawback of this method, however, is that it is based on reference data. When they are obtained for one single set of parameter values, the resulting model can reproduce the reference dynamics very accurately but generally lack of robustness away from the reference state. It is therefore crucial to enlarge the validity range of these models beyond the parameter values for which they were derived. This paper presents two strategies based on shape sensitivity analysis to partially address this limitation of the POD for parameters that define the geometry of the problem at hand (design or shape parameters.) We first detail the methodology to compute both the POD modes and their Lagrangian sensitivities with respect to shape parameters. From them, we derive improved reduced-order bases to approximate a class of solutions over a range of parameter values. Secondly, we demonstrate the efficiency and limitations of these approaches on two typical flow problems: (1) the one-dimensional Burgers' equation; (2) the two-dimensional flows past a square cylinder over a range of incidence angles.

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Verified predictions of shape sensitivities in wall-bounded turbulent flows by an adaptive finite-element method

Cited by 5 publications

References 49 publications

Accurate and robust adaptive mesh refinement for aerodynamic simulation with multi‐block structured curvilinear mesh

Accurate and robust adaptive mesh refinement for aerodynamic simulation with multi‐block structured curvilinear mesh

Anisotropic mesh adaptation driven by a recovery‐based error estimator for shallow water flow modeling

Reduced-order models for parameter dependent geometries based on shape sensitivity analysis

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