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

Summary An enhanced goal‐oriented mesh adaptation method is presented based on aerodynamic functional total derivatives with respect to mesh nodes in a Reynolds‐Averaged Navier‐Stokes (RANS) finite‐volume mono‐block and non‐matching multi‐block‐structured grid framework. This method falls under the category of methods involving the adjoint vector of the function of interest. The contribution of a Spalart–Allmaras turbulence model is taken into account through its linearization. Meshes are adapted accordingly to the proposed indicator. Applications to 2D RANS flow about a RAE2822 airfoil in transonic, and detached subsonic conditions are presented for the drag coefficient estimation. The asset of the proposed method is patent. The obtained 2D anisotropic mono‐block mesh well captures flow features as well as global aerodynamic functionals. Interestingly, the constraints imposed by structured grids may be relaxed by the use of non‐matching multi‐block approach that limits the outward propagation of local mesh refinement through all of the computational domain. The proposed method also leads to accurate results for these multi‐block meshes but at a fraction of the cost. Finally, the method is also successfully applied to a more complex geometry, namely, a mono‐block mesh in a 3D RANS transonic flow about an M6 wing. Copyright © 2016 John Wiley & Sons, Ltd.

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“…This value is in line with Li et al . Higher and lower tolerances are also considered in literature.…”

Section: Application To 2d Rans Flow About a Rae2822 Airfoilsupporting

confidence: 91%

Mono‐block and non‐matching multi‐block structured mesh adaptation based on aerodynamic functional total derivatives for RANS flow

Resmini

Peter

Lucor

2016

Numerical Methods in Fluids

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“…where S N is an artificial source term that can be obtained combining equations (24), (25) and (26):…”

Section: The Coarse-grid Nonlinear Problem Holdsmentioning

confidence: 99%

A p-multigrid strategy with anisotropic p-adaptation based on truncation errors for high-order discontinuous Galerkin methods

Rueda-Ramírez

Manzanero

Ferrer

et al. 2019

Journal of Computational Physics

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High-order discontinuous Galerkin methods have become a popular technique in computational fluid dynamics because their accuracy increases spectrally in smooth solutions with the order of the approximation. However, their main drawback is that increasing the order also increases the computational cost. Several techniques have been introduced in the past to reduce this cost. On the one hand, local mesh adaptation strategies based on error estimation have been proposed to reduce the number of degrees of freedom while keeping a similar accuracy. On the other hand, multigrid solvers may accelerate time marching computations for a fixed number of degrees of freedom.In this paper, we combine both methods and present a novel anisotropic p-adaptation multigrid algorithm for steady-state problems that uses the multigrid scheme both as a solver and as an anisotropic error estimator. To achieve this, we show that a recently developed anisotropic truncation error estimator [1, A. M. Rueda-Ramírez, G. Rubio, E. Ferrer, E. Valero, Truncation Error Estimation in the p-Anisotropic Discontinuous Galerkin Spectral Element Method, Journal of Scientific Computing] is perfectly suited to be performed inside the multigrid cycle with negligible extra cost. Furthermore, we introduce a multi-stage p-adaptation procedure which reduces the computational time when very accurate results are required.The proposed methods are tested for the compressible Navier-Stokes equations, where we investigate two cases. First, the 2D boundary layer flow on a flat plate is studied to assess accuracy and computational cost of the algorithm, where a speed-up of 816 is achieved compared to the traditional explicit method. Second, the 3D flow around a sphere is simulated and used to test the anisotropic properties of the proposed method, where a speed-up of 152 is achieved compared to the explicit method. The proposed multi-stage procedure achieved a speed-up of 2.6 in comparison to the single-stage method in highly accurate simulations.

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“…In the following, a brief description of the adaptation procedure is given. Previous studies of the application of this methodology to mesh adaptation for the Euler equations are given in Fraysse et al 30 Here, this work is extended to more complex configurations: RANS equations using hybrid meshes.…”

Section: Mesh Adaptationmentioning

confidence: 99%

Mesh adaptation and higher order extrapolation of the Reynolds-averaged Navier–Stokes equations using τ-estimation

Fraysse

Vicente

Valero

2012

Proceedings of the Institution of Mechanical Engineers, Part G:

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The aim of this article is to use an accurate truncation error estimate in order to perform -extrapolation and mesh adaptation in an unstructured finite volume computational fluid dynamics solver, in the context of a posteriori error estimation. The truncation error is approximated by the so-called -estimation technique, in which a special criterion is defined in order to account for the finite volume discretisation. It is shown that an accurate truncation error evaluation can be obtained on arbitrary geometries as long as restriction of the solution from the fine-to-coarse grid is accurate and the coarse grid possesses the same quality requirements as the fine grid. The accuracy of the truncation error estimation is successfully verified on Euler and Reynolds-averaged Navier-Stokes equations using the method of manufactured solutions. Then, mesh adaptation is performed on aerodynamic configurations where a good improvement of the force coefficients with respect to a classic feature-based indicator is obtained, at a lower cost than performing global refinement.

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

Cited by 27 publications

References 40 publications

Mono‐block and non‐matching multi‐block structured mesh adaptation based on aerodynamic functional total derivatives for RANS flow

Mono‐block and non‐matching multi‐block structured mesh adaptation based on aerodynamic functional total derivatives for RANS flow

A p-multigrid strategy with anisotropic p-adaptation based on truncation errors for high-order discontinuous Galerkin methods

Mesh adaptation and higher order extrapolation of the Reynolds-averaged Navier–Stokes equations using τ-estimation

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