Journal of computational fluids engineering (한국전산유체공학회지)

Korean Society of Computational Fluids Engineering (한국전산유체공학회)
권호 표지
DOI QR코드

DOI QR Code

DEVELOPMENT OF A HIGH-ORDER IMPLICIT DISCONTINUOUS GALERKIN METHOD FOR SOLVING COMPRESSIBLE NAVIER-STOKES EQUATIONS

압축성 Navier-Stokes 방정식 해를 위한 고차 정확도 내재적 불연속 갤러킨 기법의 개발

  • 최재훈 (한국과학기술원 대학원 항공우주공학과) ;
  • 이희동 (한국과학기술원 대학원 항공우주공학과) ;
  • 권오준 (한국과학기술원 항공우주공학과)
  • Received : 2011.04.12
  • Accepted : 2011.12.21
  • Published : 2011.12.31
Download PDF
⟨ Previous Next ⟩

Abstract

A high-order discontinuous Galerkin method for the two-dimensional compressible Navier-Stokes equations was developed on unstructured triangular meshes. For this purpose, the BR2 methd(the second Bassi and Rebay discretization) was adopted for space discretization and an implicit Euler backward method was used for time integration. Numerical tests were conducted to estimate the convergence order of the numerical solutions of the Poiseuille flow for which analytic solutions are available for comparison. Also, the flows around a flat plate, a 2-D circular cylinder, and an NACA0012 airfoil were numerically simulated. The numerical results showed that the present implicit discontinuous Galerkin method is an efficient method to obtain very accurate numerical solutions of the compressible Navier-Stokes equations on unstructured meshes.

Keywords

References

  1. 2003, Levy, D.W. et al., "Data summary from the first AIAA computational fluid dynamics drag prediction workshop," Journal of Aircraft, Vol.42, No.5, pp.875-882.
  2. 2004, Laflin, K.R. et al., "Summary of data from the second AIAA CFD drag prediction workshop," AIAA Paper 2004-0555.
  3. 2007, Morrison, J.H. and Hemsch, M.J., "Statistical analysis of CFD solutions from the third AIAA drag prediction workshop," AIAA Paper 2007-254.
  4. 2007, Vassberg, J.C. et al,. "Summary of the third AIAA CFD drag prediction workshop," AIAA Paper 2007-260.
  5. 2003, Vassberg, J.C. et al,. "Grid generation requirements for accurate drag predictions based on OVERFLOW calculations," AIAA Paper 2003-4124.
  6. 2000, Cockburn, B. et al., "Discontinuous Galerkin method theory, computation and applications," Lecture Notes in Computational Science and Engineering, Vol.11, Springer, Berlin.
  7. 2001, Cockburn, B. and Shu, C.W., "Runge-Kutta discontinuous Galerkin methods for convection-dominated problems," Journal of Scientific Computing, Vol.16, No.3, pp.173-261. https://doi.org/10.1023/A:1012873910884
  8. 1997, Bassi, F. and Rebay, S., "High order accurate discontinuous finite element solution of the 2D Euler equation," Journal of Computational Physics, Vol.138, pp.251-285. https://doi.org/10.1006/jcph.1997.5454
  9. 1997, Bassi, F. et al., "A high-order accurate discontinuous finite element method for inviscid and visous turbomachinery flows," Proceedings of 2nd European Conference on Turbomachinery, Fluid Dynamics and Thermodynamics, Technologisch Instituut, Antwerpen, Belgium, pp.99-108.
  10. 1998, Cockburn, B. and Shu, C.W., "The local discontinuous Galerkin method for time-dependent convection-diffusion systems," SIAM Journal on Numerical Analysis, Vol.35, pp.2440-2463. https://doi.org/10.1137/S0036142997316712
  11. 1976, Douglas, J. and Dupont, T., "Interior penalty procedures for elliptic and parabolic galerkin methods," Lecture Notes in Phys. 58, Spinger-Verlag, Berlin.
  12. 2002, Bassi, F. and Rebay, S., "Numerical evaluation of two discontinuous Galerkin methods for the compressible Navier-Stokes equations," International Journal for Numerical Methods in Fluids, Vol.40, pp.197-207. https://doi.org/10.1002/fld.338
  13. 1981, Roe, P.L., "Approximate Riemann Solvers, Parametric Vectors, and Difference Schemes," Journal of Computational Physics, Vol.43, pp.357-372. https://doi.org/10.1016/0021-9991(81)90128-5
  14. 2002, Arnold, D.N. et al., "Unified analysis of discontinuous Galerkin methods for elliptic problems," SIAM Journal on Numerical Analysis, Vol.39, pp.1749-1779. https://doi.org/10.1137/S0036142901384162
  15. 1998, Cockburn, B. and Shu, C.W., "The Runge-Kutta Discontinuous Galerkin Finite Element Method for Conservation Laws V : Multidimensional Systems," Journal of Computational Physics, Vol.141, pp.199-224. https://doi.org/10.1006/jcph.1998.5892
  16. 2003, Tseng, Y.H. and Ferziger, J.H., "A ghost-cell immersed boundary method for flow in complex geometry," Journal of Computational Physics, Vol.192, pp.593-623. https://doi.org/10.1016/j.jcp.2003.07.024
  17. 2010, Luo, H. et al., "A reconstructed discontinuous Galerkin method for the compressible Navier-Stokes equations on arbitrary grids," Journal of Computational Physics, Vol.229, pp.6961-6978. https://doi.org/10.1016/j.jcp.2010.05.033
  18. 1997, Bassi, F. and Rebay, S., "A high-order accurate discontinuous finite element method for the numerical solution of the compressible Navier-Stokes equations," Journal of Computational Physics, Vol.131, pp.267-279. https://doi.org/10.1006/jcph.1996.5572
  19. 1987, Martinelli, L., "Calculations of viscous flows with a multigrid method," Ph.D. thesis, Dept. of Mechanical and Aerospace Engineering, Princeton University.

Cited by

  1. Implicit discontinuous Galerkin scheme for shallow water equations vol.33, pp.7, 2011, https://doi.org/10.1007/s12206-019-0625-2