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Journal of Scientific Computing

Erschienen in:

05.12.2017

Adjoint-Based Functional Correction for Unstructured Mesh Finite Volume Methods

verfasst von: Mahkame Sharbatdar, Carl Ollivier-Gooch

Erschienen in: Journal of Scientific Computing | Ausgabe 1/2018

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Abstract

The goal of this paper is to demonstrate the use of adjoint-based functional correction and mesh adaptation for aerodynamic flows with an unstructured mesh finite volume solver. A key feature of our approach is that all calculations are performed on a single mesh, unlike other error correction and mesh adaptation schemes. As using the original p-truncation error estimate is not helpful in improving the functional, we use a smoothed estimate of the truncation error to correct the functional for both inviscid and viscous flows. The correction term is based on the smoothed truncation error and the adjoint solution, with both the continuous and discrete adjoints. The same correction term is used as an adaptation indicator for goal-based mesh adaptation as well. Our results show the effectiveness of our method in improving the convergence rate for test cases of interest in computational aerodynamics.

Nächster Artikel Flux-Conservative Hermite Methods for Simulation of Nonlinear Conservation Laws

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Discretization error is the difference between the exact solution and the discrete solution.

Becker, R., Rannacher, R.: Weighted a posteriori error control in finite element methods. In: Proceedings of ENUMATH-97, Heidelberg (1998)

Larson, M.G., Barth, T.J.: A posteriori error estimation for discontinuous Galerkin approximations of hyperbolic systems. NAS technical report, number NAS-99-010 (1999)

Ainsworth, M., Oden, J.T.: A Posteriori Error Estimation in Finite Element Analysis. Wiley, Hoboken (2000)CrossRefMATH

Machiels, L., Peraire, J., Patera, A.T.: A posteriori finite element output bounds for the incompresible Navier–Stokes equations: application to a natural convection problem. J. Comput. Phys. 172, 401–425 (2001)MathSciNetCrossRefMATH

Pierce, N., Giles, M.: Adjoint and defect error bounding and correction for functional estimates. J. Comput. Phys. 200(2), 769–794 (2004)MathSciNetCrossRefMATH

Pierce, N., Giles, M.: Adjoint recovery of superconvergent functionals from PDE approximations. SIAM Rev. 42(2), 247–264 (2000)MathSciNetCrossRefMATH

Venditti, D.A., Darmofal, D.L.: Grid adaptation for functional outputs: application to two-dimensional inviscid flows. J. Comput. Phys. 175(1), 40–69 (2002)MathSciNetCrossRefMATH

Venditti, D.A., Darmofal, D.L.: Grid adaptation for functional outputs: application to two-dimensional viscous flows. J. Comput. Phys. 187, 22–46 (2003)CrossRefMATH

Venditti, D.A., Darmofal, D.L.: Adjoint error estimation and grid adaptation for functional outputs: application to quasi-one-dimensional flow. J. Comput. Phys. 164(1), 204–227 (2000)MathSciNetCrossRefMATH

10.

Ollivier-Gooch, C.F., Van Altena, M.: A high-order accurate unstructured mesh finite-volume scheme for the advection–diffusion equation. J. Comput. Phys. 181(2), 729–752 (2002)CrossRefMATH

11.

Jalali, A., Ollivier-Gooch, C.: Accuracy assessment of finite volume discretizations of diffusive fluxes on unstructured meshes. In: Proceedings of the 50th Aerospace Sciences Meeting, AIAA Paper 2012-0608. American Institute of Aeronautics and Astronautics (2012)

12.

Diskin, B., Thomas, J.L.: Accuracy analysis for mixed-element finite-volume discretization schemes. Technical report 2007-08, National Institute of Aerospace (2007)

13.

Diskin, B., Thomas, J.L., Nielsen, E.J., Nishikawa, H., White, J.A.: Comparison of node-centered and cell-centered unstructured finite-volume discretizations. Part I: viscous fluxes. In: Proceedings of the 47th Aerospace Sciences Meeting, AIAA Paper 2009-597 (2009)

14.

Sharbatdar, M., Ollivier-Gooch, C.: Eigenanalysis of truncation and discretization error on unstructured meshes. In: 21st AIAA Computational Fluid Dynamics Conference, AIAA Paper 2013-3089. American Institute of Aeronautics and Astronautics (2013)

15.

Sharbatdar, M., Jalali, A., Ollivier-Gooch, C.: Smoothed truncation error in functional error estimation and correction using adjoint methods in an unstructured finite volume method. Comput Fluids 140, 406–421 (2016)MathSciNetCrossRef

16.

Baker, T.J.: Mesh adaptation strategies for problems in fluid dynamics. Finite Elem. Anal. Des. 25, 243–273 (1997)MathSciNetCrossRefMATH

17.

Habashi, W.G., Dompierre, J., Bourgault, Y., Ait-Ali-Yahia, D., Fortin, M., Vallet, M.G.: Anisotropic mesh adaptation: towards user-independent, mesh-independent and solver-independent CFD. Part I: general principles. Int. J. Numer. Methods Fluids 32(6), 725–744 (2000)CrossRefMATH

18.

Zienkiewicz, O.C., Zhu, J.Z.: A simple error estimator and adaptive procedure for practical engineerng analysis. Int. J. Numer. Methods Eng. 24, 337–357 (1987)CrossRefMATH

19.

Sharbatdar, M, Ollivier-Gooch, C.: Anisotropic mesh adaptation: recovering quasi-structured meshes. In: Proceedings of the 51st Aerospace Science Meeting. AIAA Paper 2013-0149 (2013)

20.

Roe, P.L.: Characteristic-based schemes for the Euler equations. Ann. Rev. Fluid Mech. 18, 337–365 (1986)MathSciNetCrossRefMATH

21.

Nishikawa, H.: Beyond interface gradient: a general principle for constructing diffusion scheme. In: Proceedings of the Fortieth AIAA Fluid Dynamics Conference and Exhibit. AIAA Paper 2010-5093 (2010)

22.

Jalali, A., Sharbatdar, M., Ollivier-Gooch, C.: Accuracy analysis of unstructured finite volume discretization schemes for diffusive fluxes. Comput. Fluids 101, 220–232 (2014)MathSciNetCrossRef

23.

Michalak, C., Ollivier-Gooch, C.: Globalized matrix-explicit Newton-GMRES for the high-order accurate solution of the Euler equations. Comput. Fluids 39, 1156–1167 (2010)MathSciNetCrossRefMATH

24.

Nejat, A.: A Higher-Order Accurate Unstructured Finite Volume Newton–Krylov Algorithm for Inviscid Compressible Flows. PhD Thesis, The University of British Columbia (2007)

25.

Ollivier-Gooch, C., Nejat, A., Michalak, C.: On obtaining and verifying high-order finite-volume solutions to the Euler equations on unstructured meshes. AIAA J. 47(9), 2105–2120 (2009)CrossRef

26.

Fidkowski, K., Darmofal, D.: Review of output-based error estimation and mesh adaptation in computational fluid dynamics. AIAA J. 49(4), 673–694 (2011)CrossRef

27.

Hayashi, M., Ceze, M., Volpe, E.: Characteristic-based boundary conditions for the Euler adjoint problem. Int. J. Numer. Methods Fluids 71, 1297–1321 (2013)MathSciNetCrossRef

28.

Kautsky, J., Nichols, N.K.: Equidistributing meshes with constraints. SIAM J. Sci. Stat Comput. 1(4), 499–511 (1980)MathSciNetCrossRefMATH

29.

Ollivier-Gooch, C.: GRUMMP version 0.7.0 user’s guide. Technical report, Department of Mechanical Engineering, The University of British Columbia (2015)

30.

Argyris, J.H., Fried, I., Scharpf, D.W.: The tuba family of plate elements for the matrix displacement method. Aeronaut. J. R. Aeronaut. Soc. 72, 701–709 (1968)

31.

Ciarlet, P.G.: The Finite Element Method for Elliptic Problems. Society for Industrial and Applied Mathematics (SIAM), Philadelphia (2002)CrossRefMATH

Titel: Adjoint-Based Functional Correction for Unstructured Mesh Finite Volume Methods
verfasst von: Mahkame Sharbatdar
Carl Ollivier-Gooch
Publikationsdatum: 05.12.2017
Verlag: Springer US
Erschienen in: Journal of Scientific Computing / Ausgabe 1/2018
Print ISSN: 0885-7474
Elektronische ISSN: 1573-7691
DOI: https://doi.org/10.1007/s10915-017-0611-8

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