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AN UNSTRUCTURED STEADY COMPRESSIBLE NAVIER-STOKES SOLVER WITH IMPLICIT BOUNDARY CONDITION METHOD

내재적 경계조건 방법을 적용한 비정렬 격자 기반의 정상 압축성 Navier-Stokes 해석자

  • Baek, C. (Dept. of Aerospace Engineering, Inha Univ.) ;
  • Kim, M. (Dept. of Aerospace Engineering, Inha Univ.) ;
  • Choi, S. (Dept. of Aerospace Engineering, Inha Univ.) ;
  • Lee, S. (Dept. of Aerospace Engineering, Inha Univ.) ;
  • Kim, C.W. (Aerodynamic Research Team, Korea Aerospace Research Institute)
  • 백청 (인하대학교 항공우주공학과) ;
  • 김민수 (인하대학교 항공우주공학과) ;
  • 최선규 (인하대학교 항공우주공학과) ;
  • 이승수 (인하대학교 항공우주공학과) ;
  • 김철완 (한국항공우주연구원)
  • Received : 2016.01.18
  • Accepted : 2016.03.02
  • Published : 2016.03.31

Abstract

Numerical boundary conditions are as important as the governing equations when analyzing the fluid flows numerically. An explicit boundary condition method updates the solutions at the boundaries with extrapolation from the interior of the computational domain, while the implicit boundary condition method in conjunction with an implicit time integration method solves the solutions of the entire computational domain including the boundaries simultaneously. The implicit boundary condition method, therefore, is more robust than the explicit boundary condition method. In this paper, steady compressible 2-Dimensional Navier-Stokes solver is developed. We present the implicit boundary condition method coupled with LU-SGS(Lower Upper Symmetric Gauss Seidel) method. Also, the explicit boundary condition method is implemented for comparison. The preconditioning Navier-Stokes equations are solved on unstructured meshes. The numerical computations for a number of flows show that the implicit boundary condition method can give accurate solutions.

Keywords

Acknowledgement

Supported by : 항공우주연구원

References

  1. 1990, Hirsch, H., "Numerical computation of internal and external flows, computational methods for inviscid and viscous flows Vol.2," John Wiley & Sons Ltd, England.
  2. 1982, Thompkins, W.T. and Bush, R.H., "Boundary treatments for implicit solutions to Euler and Navier-Stokes equations," Journal of Computational Physics, Vol.48, Issue 2, pp.302-311. https://doi.org/10.1016/0021-9991(82)90052-3
  3. 1994, Luo, H., Baum, J.D., Lohner, R. and Cabello, J., "Implicit schemes and boundary conditions for compressible flows on unstructured meshes," AIAA 32nd Aerospace Sciences Meeting & Exhibit, Reno, NV, U.S.A., AIAA-94-0816.
  4. 1982, Chakravarthy, S.R., "Euler Equations Implicit Schemes and Implicit Boundary Conditions," AIAA 20th Aerospace Sciences Meeting, Olando, Florida, U.S.A., AIAA-82-0228.
  5. 1989, Choi, Y., "Computation of Low Mach Number Compressible Flow," Ph.D. Thesis, The Pennsylvania State Univeristy.
  6. 1995, Weiss, J.M. and Smith, W.A., "Preconditioning Applied to Variable and Constant Density Flows," AIAA Journal, Vol.33, No.11, pp.2050-2057. https://doi.org/10.2514/3.12946
  7. 1981, Roe, P.L., "Approximate Riemann Solvers, Parameter Vectors, and Difference Schemes," Journal of Computational Physics, Vol.43, Issue 2, pp.357-372. https://doi.org/10.1016/0021-9991(81)90128-5
  8. 1979, van Leer, B., "Towards the Ultimate Conservative Difference Scheme, V. A Second Order Sequel to Godunov's Method," J. Com. Phys., Vol.32, pp.101-136. https://doi.org/10.1016/0021-9991(79)90145-1
  9. 1995, Venkatakrishnan, V., "Convergence to Steady State Solutions of the Euler Equations on Unstructured Grids with Limiters," Journal of Computational Physics, Vol.118, Issue 1, pp.120-130. https://doi.org/10.1006/jcph.1995.1084
  10. 2003, White, Frank M., "Fluid mechanics," McGraw-Hill, NY.
  11. 1982, Ni, R.-H., "A Multiple-Grid Scheme for Solving the Euler Equations," AIAA Journal, Vol.20, No.11, pp.1565-1571. https://doi.org/10.2514/3.51220
  12. 1999, Haselbacher, A.C., "A Grid-Transparent Numerical Method for Compressible Viscous Flows on Mixed Unstructured Grids," Ph.D. Thesis, Loughborough University.
  13. 2016, NPARC Alliance Verification and Validation Archive, http://www.grc.nasa.gov/WWW/wind/valid/achieve.html.
  14. 1970, Denis, S.C.R. and Chang, G., "Numerical Solutions for Steady Flow Past a Circular Cylinder at Reynolds Numbers up to 100," Journal of Fluid Mechanics, Vol.42, Issue 3, pp.471-489. https://doi.org/10.1017/S0022112070001428
  15. 1978, Tuann, S.-Y. and Olson, M.D., "Numerical Studies of the Flow around a Circular Cylinder by a Finite Element Method," Computer and Fluids, Vol.6, Issue 4, pp.219-240. https://doi.org/10.1016/0045-7930(78)90015-4
  16. 2010, Lee, H., Kwak, E. and Lee, S., "Investigation on Characteristics of Modified Artificial Compressibility Method," KSAS 2010 Fall Conference, Jeju, Republic of Korea.
  17. 1959, Hakkinen, R.J., Greber, I., Trilling, L. and Abarbanel, S.S., "The Interaction of an Oblique Shock Wave with a Laminar Boundary Layer."