Journal of computational fluids engineering (한국전산유체공학회지)

Korean Society of Computational Fluids Engineering (한국전산유체공학회)
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Robust and Efficient LU-SGS Scheme on Unstructured Meshes: Part I - Implicit Operator

비정렬 격자계에서 강건하고 효율적인 LU-SGS 기법 개발: Part I - 내재적 연산자

  • 김주성 (한국과학기술원 항공우주공학과 대학원) ;
  • 권오준 (한국과학기술원 항공우주공학과)
  • Published : 2004.09.01
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Abstract

A study has been made for the investigation of the robustness and convergence of various implicit operators of the LU-SGS scheme using linear stability analysis. It is shown that the behavior of the implicit operator is not determined by its own characteristics, but is determined relatively depending on the dissipative property of the explicit operator. It is also shown that, as the dissipation level of the implicit operator increases, the robustness of the scheme increases, but the convergence rate can be deteriorated due to the excessive dissipation. The numerical results demonstrate that the dissipation level of the impliict operator needs to be higher than that of the explicit operator for computing stiff problems.

Keywords

References

  1. Choi, Y.-H. and Merkle, C.L., 'The Application of Preconditioning in Viscous Flows,' J. Computational Physics, Vol.105, (1993), p.207-223
  2. Pulliam, T.H., 'Artificial Dissipation Models for the Euler Equations,' AIAA J., Vol.24, No.12, (1986), pp.1931-1940
  3. Jameson, A. and Turkel, E., 'Implicit Schemes and LU Decompositions,' Mathematics of Computation, Vol.156, (1981), p.385-397
  4. Liou, M.-S. and van Leer, B., 'Choice of Implicit and Explicit Operators for the Upwind Differencing Method,' AIAA Paper 88-0624, (1988)
  5. Amaladas, J.R. and Kamath, H., 'Implicit and Multigrid Procedures for Steady-State Computations with Upwind Algorithms,' Computers and FIuids, Vol.28, (1999), p.187-212
  6. Wright, M.J, Candler, G.V., and Prampolini, M., 'Data-Parallel Lower-Upper Relaxation Method for the Navier-Stokes Equations,' AIAA J., Vol.34, No.7, (1996), p.1371-1377
  7. Oh, W.S., Kim, J.S., and Kwon, 0J., 'Numerical Simulation of Two-Dimensional Blade-Vortex Interactions Using Unstructured Adaptive Meshes,' AIAA J., Vol.40, No.2, (2002), p.474-480
  8. Roe, P.L., 'Approximate Riemann Solvers, Parameter Vectors, and Difference Schemes,' J. Computational Physics, Vol.43, (1981), p.357-372
  9. Van Leer, B., 'Flux-Vector Splitting for the Euler Equations,' Lecture Notes in Physics, Vol.170, (1982), p.507-512
  10. 김주성, 권오준, '비정렬 격자계에서 강건하고 효율적인 LU-SGS 기법 개발: Part II- 효율적인 적용,' 한국전산유체공학회지, 제9권, 제3호, (2004)
  11. Van Leer, B., Thomas, J.L., Roe, P.L., and Newsome, R.W., 'A Comparison of Numerical Flux Formulas for the Euler and Navier-Stokes Equations,' AIAA Paper 87-1104, (1987)
  12. Toro, E.F., 'Riemann Solvers and Numerical Methods for Fluid Dynamics,' Springer, 2nd ed., (1999)
  13. Hirsch, C., 'Numerical Computation of Internal and External Flows,' John Wiley & Sons, (1988)
  14. 김주성, 권오준, '비정렬 격자계에서 LU Implicit Scheme의 수렴성 및 안정성 해석: Part I - 오일러 방정식,' 항공우주학회지 게재 심사중