Discretization Error Estimation for Discontinuous Galerkin Methods using Error Transport Equations

Wang, Hongyu; Tyson, William C.; Roy, Christopher J.

doi:10.2514/6.2019-2173

Cited by 3 publications

(1 citation statement)

References 16 publications

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“…Generally this choice is made according to an estimate of the solution smoothness in an element: if it is sufficiently smooth the adaptive algorithm opts for p-enrichment, while non-smooth zones are h-refined. Some different strategies have been proposed concerning the hp-decision [14,19,[28][29][30]. In particular Mavriplis [14] determined if the solution is locally smooth or non-smooth by computing the decay rate of the Legendre expansion coefficients of the solution under the assumption that for non-smooth solutions, the discontinuities in the solutions deteriorate this decay rate.…”

Section: Introductionmentioning

confidence: 99%

hp -adaptive hybrid RANS/LES simulations for unstructured meshes with the discontinuous Galerkin method

Basile

Chapelier

Laraufie

et al. 2022

AIAA SCITECH 2022 Forum

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In this paper, an hp-adaptation strategy designed for discontinuous Galerkin methods is applied to hybrid RANS/LES simulations. The 3D hp-adaptive strategy is suited for tetrahedral and hybrid prismatic/tetrahedral meshes, and relies on a metric-based remeshing approach. The metric field and the polynomial map of the adapted meshes are built from an a posteriori error estimator which couples the measure of the energy associated with the highest-order modes and the inter-element jumps, combined with a smoothness sensor which guides the choice between hand p-adaptation. The turbulence modelling relies on a Zonal Detached Eddy Simulation approach (ZDES mode 1). The resolution requirements in terms of minimum wall spacing Δ𝑦 + are first assessed from steady RANS flat plate simulations at Reynolds 5 • 10 6 and the value of the DES constant is assessed for DG from 3D Taylor-Green vortex flow simulations at Reynolds 5000. The developed hp-adaptation algorithm is then applied to hybrid RANS/LES simulations of the PPRIME nozzle configuration at diameter-based Reynolds 10 6 , starting the adaptive process from previously RANS-adapted meshes.

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Section: Introductionmentioning

confidence: 99%

hp -adaptive hybrid RANS/LES simulations for unstructured meshes with the discontinuous Galerkin method

Basile

Chapelier

Laraufie

et al. 2022

AIAA SCITECH 2022 Forum

View full text Add to dashboard Cite

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Error transport equations implementation for discontinuous Galerkin methods

Wang

Roy²

2023

Journal of Computational Physics

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The Performance of a Gradient-Based Method to Estimate the Discretization Error in Computational Fluid Dynamics

Satyadharma

Harinaldi

2021

Computation

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Although the grid convergence index is a widely used for the estimation of discretization error in computational fluid dynamics, it still has some problems. These problems are mainly rooted in the usage of the order of a convergence variable within the model which is a fundamental variable that the model is built upon. To improve the model, a new perspective must be taken. By analyzing the behavior of the gradient within simulation data, a gradient-based model was created. The performance of this model is tested on its accuracy, precision, and how it will affect a computational time of a simulation. The testing is conducted on a dataset of 36 simulated variables, simulated using the method of manufactured solutions, with an average of 26.5 meshes/case. The result shows the new gradient based method is more accurate and more precise then the grid convergence index(GCI). This allows for the usage of a coarser mesh for its analysis, thus it has the potential to reduce the overall computational by at least by 25% and also makes the discretization error analysis more available for general usage.

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Discretization Error Estimation for Discontinuous Galerkin Methods using Error Transport Equations

Cited by 3 publications

References 16 publications

hp -adaptive hybrid RANS/LES simulations for unstructured meshes with the discontinuous Galerkin method

hp -adaptive hybrid RANS/LES simulations for unstructured meshes with the discontinuous Galerkin method

Error transport equations implementation for discontinuous Galerkin methods

The Performance of a Gradient-Based Method to Estimate the Discretization Error in Computational Fluid Dynamics

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