Maio 2014 vol. 1 num. 1 - 10th World Congress on Computational Mechanics

Full Article - Open Access.

Idioma principal

ANISOTROPIC SIMPLEX MESH ADAPTATION BY METRIC OPTIMIZATION FOR HIGHER-ORDER DG DISCRETIZATIONS OF 3D COMPRESSIBLE FLOWS

Yano, Masayuki ; Darmofal, David L. ;

Full Article:

We extend our optimization-based framework for anisotropic simplex mesh adaptation to three dimensions and apply it to high-order discontinuous Galerkin discretizations of steady-state aerodynamic flows. The framework iterates toward a mesh that minimizes the output error for a given number of degrees of freedom by considering a continuous optimization problem of the Riemannian metric field. The adaptation procedure consists of three key steps: sampling of the anisotropic error behavior using element-wise local solves; synthesis of the local errors to construct a surrogate error model in the metric space; and optimization of the surrogate model to drive the mesh toward optimality. The anisotropic adaptation decisions are entirely driven by the behavior of the a posteriori error estimate. As a result, the method handles any discretization order, naturally incorporates both the primal and adjoint solution behaviors, and robustly treats irregular features. Numerical results demonstrate the effectiveness of the adaptive high-order discretization applied to the compressible Navier-Stokes equations in three dimensions.

Full Article:

Download (PDF)

Palavras-chave: anisotropic adaptation, discontinuous Galerkin method, higher-order, dualweighted residual, compressible Navier-Stokes,

Palavras-chave:

DOI: 10.5151/meceng-wccm2012-18538

Referências bibliográficas
  • [1] F. Bassi, S. Rebay, GMRES discontinuous Galerkin solution of the compressible Navier- Stokes equations, in: K. Cockburn, Shu (eds.), Discontinuous Galerkin Methods: Theory, Computation and Applications, Springer, Berlin, 2000, pp. 197–208.
  • [2] R. Becker, R. Rannacher, An optimal control approach to a posteriori error estimation in finite element methods, in: A. Iserles (ed.), Acta Numerica, Cambridge University Press, 2001.
  • [3] M. Ceze, K. J. Fidkowski, Output-driven anisotropic mesh adaptation for viscous flows using discrete choice optimization, AIAA 2010–170 (2010).
  • [4] L. T. Diosady, D. L. Darmofal, Preconditioning methods for discontinuous Galerkin solutions of the Navier-Stokes equations, J. Comput. Phys. 228 (2009) 3917–3935.
  • [5] K. Fidkowski, D. Darmofal, Review of output-based error estimation and mesh adaptation in computational fluid dynamics 49 (4) (2011) 673–694.
  • [6] K. J. Fidkowski, A simplex cut-cell adaptive method for high-order discretizations of the compressible Navier-Stokes equations, PhD thesis, Massachusetts Institute of Technology, Department of Aeronautics and Astronautics (Jun. 2007).
  • [7] K. J. Fidkowski, D. L. Darmofal, A triangular cut-cell adaptive method for higher-order discretizations of the compressible Navier-Stokes equations, J. Comput. Phys. 225 (2007) 1653–1672.
  • [8] R. Hartmann, P. Houston, Error estimation and adaptive mesh refinement for aerodynamic flows, in: H. Deconinck (ed.), VKI LS 2010-01: 36th CFD/ADIGMA course on hp-adaptive and hp-multigrid methods, Oct. 26-30, 2009, Von Karman Institute for Fluid Dynamics, Rhode Saint Genèse, Belgium, 2009.
  • [9] P. Houston, E. H. Georgoulis, E. Hall, Adaptivity and a posteriori error estimation for DG methods on anisotropic meshes, International Conference on Boundary and Interior Layers.
  • [10] N. Kroll, ADIGMA - a European project on the development of adaptive higher-order variational methods for aerospace applications, AIAA 2009-176 (2009).
  • [11] T. Leicht, R. Hartmann, Anisotropic mesh refinement for discontinuous Galerkin methods in two-dimensional aerodynamic flow simulations, Internat. J. Numer. Methods Fluids 56 (2008) 2111–2138.
  • [12] T. Leicht, R. Hartmann, Error estimation and anisotropic mesh refinement for 3d laminar aerodynamic flow simulations, J. Comput. Phys. 229 (2010) 7344–7360.
  • [13] A. Loseille, F. Alauzet, Continuous mesh model and well-posed continuous interpolation error estimation, INRIA RR-6846 (2009).
  • [14] A. Loseille, F. Alauzet, Optimal 3d highly anisotropic mesh adaptation based on the continuous mesh framework, in: Proceedings of the 18th International Meshing Roundtable, Springer Berlin Heidelberg, 2009.
  • [15] A. Loseille, A. Dervieux, F. Alauzet, On 3-d goal-oriented anisotropic mesh adaptation applied to inviscid flows in aeronautics, AIAA 2010-1067 (2010).
  • [16] D. J. Mavriplis, Results from the 3rd Drag Prediction Workshop using the NSU3D unstructured mesh solver, AIAA 2007-256 (2007).
  • [17] T. Michal, J. Krakos, Anisotropic mesh adaptation through edge primitive operations, AIAA 2012-159 (2012).
  • [18] X. Pennec, P. Fillard, N. Ayache, A Riemannian framework for tensor computing, Int. J. Comput. Vision 66 (1) (2006) 41–66.
  • [19] P.-O. Persson, J. Peraire, Newton-GMRES preconditioning for discontinuous Galerkin discretizations of the Navier-Stokes equations, SIAM J. Sci. Comput. 30 (6) (2008) 2709–2722.
  • [20] R. Rannacher, Adaptive Galerkin finite element methods for partial differential equations, Journal of Computational and Applied Mathematics 128 (2001) 205–233.
  • [21] P. L. Roe, Approximate Riemann solvers, parameter vectors, and difference schemes, J. Comput. Phys. 43 (2) (1981) 357–372.
  • [22] Y. Saad, M. H. Schultz, GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems, SIAM Journal on Scientific and Statistical Computing 7 (3) (1986) 856–869.
  • [23] D. A. Venditti, D. L. Darmofal, Anisotropic grid adaptation for functional outputs: Application to two-dimensional viscous flows, J. Comput. Phys. 187 (1) (2003) 22–46.
  • [24] Z. J. Wang, 1st international workshop on high-order CFD methods, http://zjw.public.iastate.edu/hiocfd.html.
  • [25] M. Yano, An optimization framework for adaptive higher-order discretizations of partial differential equations on anisotropic simplex meshes, PhD thesis, Massachusetts Institute of Technology, Department of Aeronautics and Astronautics (Jun. 2012).
  • [26] M. Yano, D. Darmofal, An optimization framework for anisotopic simplex mesh adaptation, J. Comput. Phys. (submitted).
  • [27] M. Yano, D. Darmofal, An optimization framework for anisotropic simplex mesh adaptation: application to aerodynamic flows, AIAA 2012–0079 (Jan. 2012).
Como citar:

Yano, Masayuki; Darmofal, David L.; "ANISOTROPIC SIMPLEX MESH ADAPTATION BY METRIC OPTIMIZATION FOR HIGHER-ORDER DG DISCRETIZATIONS OF 3D COMPRESSIBLE FLOWS", p. 1770-1785 . In: In Proceedings of the 10th World Congress on Computational Mechanics [= Blucher Mechanical Engineering Proceedings, v. 1, n. 1]. São Paulo: Blucher, 2014.
ISSN 2358-0828, DOI 10.5151/meceng-wccm2012-18538

últimos 30 dias | último ano | desde a publicação


downloads


visualizações


indexações