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

Full Article - Open Access.

Idioma principal

DEVELOPMENT OF A 3D COMPRESSIBLE NAVIER-STOKES SOLVER BASED ON A DG FORMULATION WITH SUB-CELL SHOCK CAPTURING STRATEGY FOR FULLY HYBRID UNSTRUCTURED MESHES

Cantão, R. F. ; Silva, C. A. C. ; Bigarella, E. D. V. ; Jr., A. C. Nogueira ;

Full Article:

The development of a CFD tool based on Discontinuous Galerkin discretization is reported. This tool solves the compressible, Reynolds-Averaged Navier-Stokes equations for three-dimensional, hybrid unstructured meshes. This tool is aimed at complex aerospace applications, thus requiring advanced turbulence models and an efficient numerical framework to enhance computational performance and numerical accuracy for high Reynolds number, high Mach number flows. Inviscid fluxes are computed by upwind Roe or HLLC schemes and viscous fluxes are computed using BR1 or BR2 formulations. A 2nd-order accurate, 5- stage, explicit Runge-Kutta time-stepping scheme is used to march the equations in time. The solver computational efficiency, convergence, accuracy and parallel scalability are addressed through flow simulations over typical validation test cases. Convergence rates for increasing degrees of freedom are shown to be asymptotic, with numerical errors compatible to DG schemes. Parallelism is shown to be conformant with the expected scalability behaviour. For the aerospace applications considered in this paper, acceptable agreement with theoretical or experimental results is obtained at adequate computational costs.

Full Article:

Download (PDF)

Palavras-chave: Discontinuous Galerkin, compressible RANS, hybrid meshes, aerospace applications,

Palavras-chave:

DOI: 10.5151/meceng-wccm2012-18153

Referências bibliográficas
  • [1] J. D. Anderson, Jr. Fundamentals of Aerodynamics, chapter 15, page 647. McGraw-Hill International Editions, New York, NY, USA, second edition, 199
  • [2] J. D. Anderson, Jr. Fundamentals of Aerodynamics, chapter 17, pages 723–729. McGraw-Hill International Editions, New York, NY, USA, second edition, 1991.
  • [3] D. N. Arnold, F. Brezzi, B. Cockburn, , and L. D. Marini. Unified analysis of discontinuous galerkin methods for elliptic problems. SIAM Journal on Numerical Analysis, 39(5):1749–1779, 2002.
  • [4] D. N. Arnold, F. Brezzi, B. Cockburn, and D. Marini. Discontinuous Galerkin Methods for Elliptic problems. In C.-W. Shu B. Cockburn amd G. Karniadakis, editor, Discontinuous Galerkin Methods: theory, computation and applications, pages 89–101. Springer, 2000.
  • [5] G. E. Barter. Shock Capturing with PDE-Based Artificial Viscosity for an Adaptive, Higher-Order Discontinuous Galerkin Finite Element Method. PhD thesis, Massachusetts Institute of Technology, June 2008.
  • [6] F. Bassi and S. Rebay. Gmres discontinuous galerkin solution of the compressible navier-stokes equations. In Cockburn, Karniadakis, and Shu, editors, Discontinuous Galerkin Methods: Theory, Computation and Applications, pages 197–208. Springer, Berlin, 2000.
  • [7] P. Batten, M. A. Leschziner, and U. C. Goldberg. Average-state Jacobians and implicit methods for compressible viscous and turbulent flows. Journal of Computational Physics, 137(1):38–78, Oct. 199
  • [8] E. D. V. Bigarella. Advanced Turbulence Modelling for Complex Aerospace Applications. PhD thesis, Instituto Tecnológico de Aeronáutica, São Jos´e dos Campos, SP, Brazil, Oct. 2007.
  • [9] E. D. V. Bigarella and J. L. F. Azevedo. A study of convective flux computation schemes for aerodynamic flows. In 43rd AIAA Aerospace Sciences Meeting and Exhibit, AIAA Paper No. 2005-0633, Reno, NV, Jan. 2005.
  • [10] J. S. Hesthaven and T. C. Warburton. Nodal Discontinuous Galerkin Methods – Algorithms, Analysis and Applications, volume 54 of Texts in Applied Mathematics. Springer, 1st edition, 2008.
  • [11] A. Jameson, W. Schmidt, and E. Turkel. Numerical solution of the Euler equations by finite volume methods using Runge-Kutta time-stepping schemes. In 14th AIAA Fluid and Plasma Dynamics Conference, AIAA Paper No. 81-1259, Palo Alto, CA, June 1981.
  • [12] G. E. Karniadakis and S. J. Sherwin. Spectral/hp Element Methods for Computational Fluid Dynamics. Oxford University Press, Oxford, 2nd edition, 2005.
  • [13] D. J. Mavriplis. Accurate multigrid solution of the Euler equations on unstructured and adaptive meshes. AIAA Journal, 28(2):213–221, Feb. 1990.
  • [14] P. O. Persson and J. Peraire. Sub-cell shock capturing for discontinuous galerkin methods. In 44th AIAA Aerospace Sciences Meeting and Exhibit, AIAA Paper No. 2006-112. AIAA, 2006.
  • [15] Patrick J Roache. Verification and Validation in Computational Science and Engineering. Hermosa Publishers, Albuquerque, NM, USA, 1998.
  • [16] P. L. Roe. Approximate Riemann solvers, parameter vectors, and difference schemes. Journal of Computational Physics, 43(2):357–372, Oct. 1981.
  • [17] B. van Leer. Towards the ultimate conservative difference scheme. V. A second-order sequel to Godunov’s method. Journal of Computational Physics, 32(1):101–136, July 1979.
Como citar:

Cantão, R. F.; Silva, C. A. C.; Bigarella, E. D. V.; Jr., A. C. Nogueira; "DEVELOPMENT OF A 3D COMPRESSIBLE NAVIER-STOKES SOLVER BASED ON A DG FORMULATION WITH SUB-CELL SHOCK CAPTURING STRATEGY FOR FULLY HYBRID UNSTRUCTURED MESHES", p. 868-885 . 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-wccm2012-18153

últimos 30 dias | último ano | desde a publicação


downloads


visualizações


indexações