Adjoint-based error estimation and adaptive mesh refinement for the RANS and k–ω turbulence model equations

Hartmann, Ralf; Held, Joachim; Leicht, Tobias

doi:10.1016/j.jcp.2010.10.026

Cited by 80 publications

(69 citation statements)

References 38 publications

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“…, n el is set, aiming at obtaining a uniform error distribution in the whole domain, and minimizing possible pollution effects. Nevertheless, the stopping criterion for the adaptive procedure is based on checking the error only at the elements in the area of interest Ω int , see Equation (9).…”

Section: Evaluation Of the Naca 0012 Aerodynamic Characteristicsmentioning

confidence: 99%

“…The importance of adaptive simulations in the field of computational fluid dynamics (CFD) has been pointed out by various authors in the last years [1][2][3][4][5][6][7][8][9]. Non-uniform discretizations, adapted to local flow features, are necessary to capture strong variations in the solution, shocks, sharp fronts or boundary layers, while keeping a coarser mesh where it is possible.…”

Section: Introductionmentioning

confidence: 99%

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Hybridizable Discontinuous Galerkin with degree adaptivity for the incompressible Navier–Stokes equations

2014

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A degree adaptive Hybridizable Discontinuous Galerkin (HDG) method for the solution of the incompressible Navier-Stokes equations is presented. The key ingredient is an accurate and computationally inexpensive a posteriori error estimator based on the super-convergence properties of HDG. The error estimator drives the local modification of approximation degree in the elements and faces of the mesh, aimed at obtaining a uniform error distribution below a user-given tolerance in a given are of interest. Three 2D numerical examples are presented. High efficiency of the proposed error estimator is found, and an important reduction of the computational effort is shown with respect to non-adaptive computations, both for steady state and transient simulations.

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Section: Evaluation Of the Naca 0012 Aerodynamic Characteristicsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Hybridizable Discontinuous Galerkin with degree adaptivity for the incompressible Navier–Stokes equations

2014

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“…This scheme is of particular interest because (in some cases) it yields explicit time-step limits which are more than 2x larger than those of the collocation-based nodal DG scheme 18 . For this scheme, and for each set of nodal points, L2 errors in the energy E are shown in Table ( 6). In addition, contours of the density obtained with the α-optimized points for the case ofÑ = 8 and p = 3 are shown in Figure (9).…”

Section: B Flow Generated By a Time-dependent Source Termmentioning

confidence: 99%

“…In particular, high-order methods have been successfully employed to simulate flows over flapping wings 2,3 , rotorcraft 4 , turbine blades 5 , and high-lift devices 6 . Despite their success in these settings, they have yet to be adopted by a wide community of fluid-dynamicists.…”

Section: Introductionmentioning

confidence: 99%

Nodal Points and the Nonlinear Stability of High-Order Methods for Unsteady Flow Problems on Tetrahedral Meshes

Williams

Jameson

2013

21st AIAA Computational Fluid Dynamics Conference

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High-order methods have the potential to efficiently generate accurate solutions to fluid dynamics problems of practical interest. However, high-order methods are less robust than lower-order methods, as they are less dissipative, making them more susceptible to spurious oscillations and aliasing driven instabilities that arise during simulations of nonlinear phenomena. An effective approach for addressing this issue comes from noting that, for nonlinear problems, the stability of high-order nodal methods is significantly effected by the locations of the nodal points. In fact, in 1D and 2D, it has been shown that placing the nodal points at the locations of quadrature points reduces aliasing errors and improves the robustness of high-order schemes. In this paper, the authors perform an investigation of a particular set of nodal points whose locations coincide with quadrature points. Analysis is performed in order to determine the conditioning of these points and their suitability for interpolation. Thereafter, numerical experiments are performed on several canonical 3D problems in order to show that this set of nodal points is effective in reducing aliasing errors and promoting nonlinear stability.

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“…Typical values for this constant of proportionality are 2 to 3, with significantly lower values reported for highly nonlinear functions. 56,57 For the solver used in this work, the adjoint solution is typically found an order of magnitude faster than the flow solution.…”

Section: Va1 Validity Of Optimizationmentioning

confidence: 99%

Mixed Aleatory/Epistemic Uncertainty Quantification for Hypersonic Flows via Gradient-Based Optimization and Surrogate Models

Lockwood

Anitescu

Mavriplis

2012

50th AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition

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The use of optimization for the propagation of mixed epistemic/aleatory uncertainties is demonstrated within the context of hypersonic flows. Specifically, this work focuses on strategies applicable for models where input parameters can be divided into a set of variables containing only aleatory uncertainties and a set with epistemic uncertainties. With the input parameters divided in this way, uncertainty due to the epistemic variables is propagated via a constrained optimization approach, while the uncertainty due to aleatory variables is propagated via sampling. A statistics-of-intervals approach is proposed in which the constrained optimization results are treated as a random variable and multiple optimizations are performed to quantify the aleatory uncertainty. In order to reduce the total number of optimizations required, a surrogate is employed to model the variation of the optimization results with respect to the aleatory variables, and exhaustive sampling is performed on this surrogate to determine the desired statistics. The properties of the statistics-of-intervals approach are demonstrated by using the Fay-Riddell stagnation heating correlations and compared with a competing method based on uncertain optimization. Additionally, the statistics-of-intervals approach is demonstrated for mixed epistemic/aleatory uncertainty quantification on a real gas computational fluid dynamic simulation.

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Adjoint-based error estimation and adaptive mesh refinement for the RANS and k–ω turbulence model equations

Cited by 80 publications

References 38 publications

Hybridizable Discontinuous Galerkin with degree adaptivity for the incompressible Navier–Stokes equations

Hybridizable Discontinuous Galerkin with degree adaptivity for the incompressible Navier–Stokes equations

Nodal Points and the Nonlinear Stability of High-Order Methods for Unsteady Flow Problems on Tetrahedral Meshes

Mixed Aleatory/Epistemic Uncertainty Quantification for Hypersonic Flows via Gradient-Based Optimization and Surrogate Models

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