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High-order discontinuous Galerkin solver on hybrid anisotropic meshes for laminar and turbulent simulations

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  • College of Aeronautics Science and Engineering, Beijing University of Aeronautics and Astronautics, Beijing 100191, P. R. China

Received date: 2013-01-01

  Revised date: 2013-08-01

  Online published: 2014-07-01

Supported by

Project supported by the National Basic Research Program of China (No. 2009CB724104)

Abstract

Efficient and robust solution strategies are developed for discontinuous Galerkin (DG) discretization of the Navier-Stokes (NS) and Reynolds-averaged NS (RANS) equations on structured/unstructured hybrid meshes. A novel line-implicit scheme is devised and implemented to reduce the memory gain and improve the computational efficiency for highly anisotropic meshes. A simple and effective technique to use the mod- ified Baldwin-Lomax (BL) model on the unstructured meshes for the DG methods is proposed. The compact Hermite weighted essentially non-oscillatory (HWENO) limiters are also investigated for the hybrid meshes to treat solution discontinuities. A variety of compressible viscous flows are performed to examine the capability of the present high- order DG solver. Numerical results indicate that the designed line-implicit algorithms exhibit weak dependence on the cell aspect-ratio as well as the discretization order. The accuracy and robustness of the proposed approaches are demonstrated by capturing com- plex flow structures and giving reliable predictions of benchmark turbulent problems.

Cite this article

Zhen-hua JIANG;Chao YAN;Jian YU . High-order discontinuous Galerkin solver on hybrid anisotropic meshes for laminar and turbulent simulations[J]. Applied Mathematics and Mechanics, 2014 , 35(7) : 799 -812 . DOI: 10.1007/s10483-014-1834-9

References

[1] Cockburn, B. and Shu, C. W. The Runge-Kutta discontinuous Galerkin method for conservation laws V: multidimensional systems. J. Comput. Phys., 141, 199-224 (1998)
[2] Cockburn, B., Karniadakis, G., and Shu, C. W. The development of discontinuous Galerkin method. Discontinuous Galerkin Methods, Lecture Notes in Computational Science and Engineering, Springer, New York, 3-50 (2000)
[3] Nastase, C. R. and Mavriplis, D. J. High-order discontinuous Galerkin methods using an hp- multigrid approach. J. Comput. Phys., 213, 330-357 (2006)
[4] Fidkowski, K. J., Oliver, T. A., Lu, J., and Darmofal, D. L. P-multigrid solution of high-order discontinuous Galerkin discretizations of the compressible Navier-Stokes equations. J. Comput. Phys., 207, 92-113 (2005)
[5] Shahbazi, K., Mavriplis, D. J., and Burgess, N. K. Multigrid algorithms for high-order discontinu- ous Galerkin discretizations of the compressible Navier-Stokes equations. J. Comput. Phys., 228, 7917-7940 (2009)
[6] Diosady, L. T. and Darmofal, D. L. Preconditioning methods for discontinuous Galerkin solutions of the Navier-Stokes equations. J. Comput. Phys., 228, 3917-3935 (2009)
[7] Haga, T., Gao, H., and Wang, Z. J. Efficient solution techniques for high-order methods on 3D anisotropic hybrid meshes. The 49th AIAA Aerospace Sciences Meeting Induding the New Horizons Forum and Aerospace Exposition, Curran Associates, Florida (2011)
[8] Burgess, N. K., Nastase, C. R., and Mavriplis, D. J. Efficient solution techniques for discontinuous Galerkin discretizations of the Navier-Stokes equations on hybrid anisotropic meshes. The 48th AIAA Aerospace Sciences Meeting Induding the New Horizons Forum and Aerospace Exposition, American Institute of Aeronautics and Astronautics, Florida (2010)
[9] Mavriplis, D. J. Multigrid strategies for viscous flow solvers on anisotropic unstructured meshes. J. Comput. Phys., 145, 141-165 (1998)
[10] Bassi, F., Crivellini, A., Rebay, S., and Savini, M. Discontinuous Galerkin solution of the Reynolds- averaged Navier-Stokes and k-! turbulence model equations. Computers and Fluids, 34, 507-540 (2005)
[11] Landmann, B., Kessler, M., Wagner, S., and Kramer, E. A parallel, high-order discontinuous Galerkin code for laminar and turbulent flows. Computers and Fluids, 37(4), 427-438 (2008)
[12] Burgess, N. K. and Mavriplis, D. J. Robust computation of turbulent flows using a discontinuous Galerkin method. The 50th AIAA Aerospace Sciences Meeting Induding the New Horizons Forum and Aerospace Exposition, American Institute of Aeronautics and Astronautics, Tennessee (2012)
[13] Li, X., Yang, Y., Hao, H., and Jiao, J. Exploring high-order accurate discontinuous Galerkin method for numerical solution of compressible Reynolds-averaged Navier-Stokes (RANS) equa- tions (in Chinese). Journal of Northwestern Polytechnical University, 30(3), 407-411 (2012)
[14] Mavriplis, D. J. Algebraic turbulence modeling for unstructured and adaptive meshes. AIAA Journal, 29, 2086-2093 (1991)
[15] Jiang, Z., Yan, C., Yu, J., and Yuan, W. Hermite WENO-based limiters for high order discontinuous Galerkin method on unstructured grids. Acta Mechanica Sinica, 28(2), 1-12 (2012)
[16] Bassi, F. and Rebay, S. GMRES discontinuous Galerkin solution of the compressible Navier-Stokes equations. Lecture Note in Computational Science and Engineering, Springer-Verlag, New York, 197-208 (2000)
[17] Zhao, R., Yan, C., and Yu, J. New kind Baldwin-Lomax turbulence model under the limit of entropy (in Chinese). Journal of Beijing University of Aeronautics and Astronautics, 38(2), 175- 180 (2012)
[18] Nielsen, E. J., Anderson, W. K., and Walters, R. W. Application of Newton-Krylov methodol- ogy to a three-dimensional unstructured Euler codes. The 12th Computational Fluid Dynamics Conference, American Institute of Aeronautics and Astronautics, California (1995)
[19] Bassi, F. and Rebay, S. A high-order accurate discontinuous finite element method for the nu- merical solution of the compressible Navier-Stokes equations. J. Comput. Phys., 131, 267-279 (1997)
[20] Cook, P. H., McDonald, M. A., and Firmin, M. C. P. Aerofoil RAE2822 Pressure Distributions, Boundary Layer and Wake Measurements, AGARD AR-138, Research and Technology Organi- sation, Neuilly-sur-Seine (1979)
[21] Klausmeyer, S. M. and Lin, J. C. Comparative results from a CFD challenge over a 2D three- element high-lift airfoil. NASA Technical Memorandum, Microfoche, Washington, D. C. (1997)
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