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

doi:10.1007/s10483-014-1834-9

Applied Mathematics and Mechanics (English Edition) ›› 2014, Vol. 35 ›› Issue (7): 799-812.doi: https://doi.org/10.1007/s10483-014-1834-9

• 论文 • 下一篇

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

姜振华, 阎超, 于剑

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

收稿日期:2013-01-01 修回日期:2013-08-01 出版日期:2014-07-01 发布日期:2014-07-01
通讯作者: Zhen-hua JIANG, Ph.D., E-mail:zhenhua122122@163.com E-mail:zhenhua122122@163.com
基金资助:
Project supported by the National Basic Research Program of China (No. 2009CB724104)

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

Zhen-hua JIANG, Chao YAN, Jian YU

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

Received:2013-01-01 Revised:2013-08-01 Online:2014-07-01 Published:2014-07-01
Supported by:
Project supported by the National Basic Research Program of China (No. 2009CB724104)

摘要/Abstract

摘要： 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.

关键词: discontinuous Galerkin (DG) method, implicit method, Baldwin-Lomax (BL) model, high order accuracy, structured/unstructured hybrid mesh

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.

Key words: structured/unstructured hybrid mesh, discontinuous Galerkin (DG) method, implicit method, Baldwin-Lomax (BL) model, high order accuracy

中图分类号:

O357.3

姜振华;阎超;于剑. High-order discontinuous Galerkin solver on hybrid anisotropic meshes for laminar and turbulent simulations[J]. Applied Mathematics and Mechanics (English Edition), 2014, 35(7): 799-812.

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 (English Edition), 2014, 35(7): 799-812.

参考文献

[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)

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

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

PDF

可视化

被引次数

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 3

编辑推荐

Metrics

本文评价

[1]	Ziqiang CHENG, Shihao LIU, Yan JIANG, Jianfang LU, Mengping ZHANG, Shuhai ZHANG. A high order boundary scheme to simulate complex moving rigid body under impingement of shock wave[J]. Applied Mathematics and Mechanics (English Edition), 2021, 42(6): 841-854.
[2]	M. M. RASHIDI;A. HOSSEINI;I. POP;S. KUMAR;N. FREIDOONIMEHR. Comparative numerical study of single and two-phase models of nanofluid heat transfer in wavy channel[J]. Applied Mathematics and Mechanics (English Edition), 2014, 35(7): 831-848.
[3]	羊丹平. A COUPLING METHOD OF DIFFERENCE WITH HIGH ORDER ACCURACY AND BOUNDARY INTEGRAL EQUATION FOR EVOLUTIONARY EQUATION AND ITS ERROR ESTIMATES[J]. Applied Mathematics and Mechanics (English Edition), 1991, 12(9): 891-905.