Adjoint-based error estimation and grid adaptation for functional outputs: Application to two-dimensional, inviscid, incompressible flows

Balasubramanian, R.; Newman, James C.

doi:10.1016/j.compfluid.2008.04.003

Cited by 15 publications

(17 citation statements)

References 31 publications

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“…The interested reader is referred to References [42,57] for a complete discussion on the solution procedure, linearization of flux limiters, parallel implementation and demonstration of consistency of linearization. By introducing a perturbation Q h to the fine-mesh solution Q h , and performing a Taylor's series expansion of…”

Section: Discrete Adjoint Analysismentioning

confidence: 99%

“…Linear and quadratic basis functions are considered with cubic spline [47] weights. Weight functions are defined with compact circular or rectangular supports [47,57]. Once the supports are built, weights are applied, either isotropically as radial weights, or anisotropically as tensor product weights.…”

Section: Prolongation Operatorsmentioning

confidence: 99%

“…The adaptive mesh library is based on References [50][51][52] and performs isotropic h-refinement of the elements. The refinement template [53,57] controls the pattern of subdivision of the mesh elements. The reader is referred to Reference [57] for the refinement patterns of different element types used in the study.…”

Section: Adaptation Mechanicsmentioning

confidence: 99%

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Comparison of adjoint‐based and feature‐based grid adaptation for functional outputs

Balasubramanian

Newman

2006

Numerical Methods in Fluids

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SUMMARYAdjoint-based and feature-based grid adaptive strategies are compared for their robustness and effectiveness in improving the accuracy of functional outputs such as lift and drag coefficients. The output-based adjoint approach strives to improve the adjoint error estimates that relate the local residual errors to the global error in an output function via adjoint variables as weight functions. A conservative adaptive indicator that takes into account the residual errors in both the primal (flow) and dual (adjoint) solutions is implemented for the adjoint approach. The physics-based feature approach strives to identify and resolve significant features of the flow to improve functional accuracy. Adaptive indicators that represent expansions and compressions in the flow direction and gradients normal to the flow direction are implemented for the feature approach. The adaptive approaches are compared for functional outputs of three-dimensional arbitrary Mach number flow simulations on mixed-element unstructured meshes. Grid adaptation is performed with h-refinement and results are presented for inviscid, laminar and turbulent flows.

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Section: Discrete Adjoint Analysismentioning

confidence: 99%

Section: Prolongation Operatorsmentioning

confidence: 99%

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Comparison of adjoint‐based and feature‐based grid adaptation for functional outputs

Balasubramanian

Newman

2006

Numerical Methods in Fluids

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“…Hartmann [27], Balasubramanian and Newman [3]. These techniques require the selection of a functional target (e.g.…”

Section: Introductionmentioning

confidence: 99%

Adaptation strategies for high order discontinuous Galerkin methods based on Tau-estimation

Kompenhans

Rubio

Ferrer

et al. 2016

Journal of Computational Physics

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In this paper three p-adaptation strategies based on the minimization of the truncation error are presented for high order discontinuous Galerkin methods. The truncation error is approximated by means of a r-estimation procedure and enables the identification of mesh regions that require adaptation. Three adaptation strategies are developed and termed a posteriori, quasi-a priori and quasi-a priori corrected. All strategies require fine solutions, which are obtained by enriching the polynomial order, but while the former needs time converged solutions, the last two rely on non-converged solutions, which lead to faster computations. In addition, the high order method permits the spatial decoupling for the estimated errors and enables anisotropic p-adaptation. These strategies are verified and compared in terms of accuracy and computational cost for the Euler and the compressible Navier-Stokes equations. It is shown that the two quasia priori methods achieve a significant reduction in computational cost when compared to a uniform polynomial enrichment. Namely, for a viscous boundary layer flow, we obtain a speedup of 6.6 and 7.6 for the quasi-a priori and quasi-a priori corrected approaches, respectively.

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“…Hartmann [Hartmann 2006], Balasubramanian and Newman [Balasubramanian 2009]. These techniques require the selection of a functional target (e.g.…”

Section: Figure 11: H- P-and H/p-refinementmentioning

confidence: 99%

Adaptation Strategies for Discontinuous Galerkin Spectral Element Methods by means of Truncation Error Estimations

Kompenhans¹

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Adjoint-based error estimation and grid adaptation for functional outputs: Application to two-dimensional, inviscid, incompressible flows

Cited by 15 publications

References 31 publications

Comparison of adjoint‐based and feature‐based grid adaptation for functional outputs

Comparison of adjoint‐based and feature‐based grid adaptation for functional outputs

Adaptation strategies for high order discontinuous Galerkin methods based on Tau-estimation

Adaptation Strategies for Discontinuous Galerkin Spectral Element Methods by means of Truncation Error Estimations

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