Fully-Implicit Decoupling Method for Incompressible Navier-Stokes Equations

비압축성 나비어-스톡스 방정식의 완전 내재적 분리 방법

  • Published : 2000.10.01


A new efficient numerical method for computing three-dimensional, unsteady, incompressible flows is presented. To eliminate the restriction of CFL condition, a fully-implicit time advancement in which the Crank-Nicolson method is used for both the diffusion and convection terms, is adopted. Based on an approximate block LU decomposition method, the velocity -pressure decoupling is achieved. The additional decoupling of the intermediate velocity components in the convection term is made for the fully -implicit time advancement scheme. Since the iterative procedures for the momentum equations are not required, the velocity components decouplings bring forth the reduction of computational cost. The second-order accuracy in time of the present numerical algorithm is ascertained by computing decaying vortices. The present decoupling method is applied to minimal channel flow unit with DNS (Direct Numerical Simulation).


Fully-Implicit Time Advancement;Velocity-Pressure Decoupling;Velocity Components Decoupling;Approximate Factorization;DNS


  1. Akselvoll, K. and Moin, P., 1995, 'Large Eddy Simulation of Turbulent Confined Coannular Jets and Turbulent Flow over a Backward Facing Step,' Report No. TF-63, Department of Mechanical Engineering, Stanford University, Stanford, CA
  2. Bell, J., Collea, P. and Glaz, H., 1989, 'A Second-Order Projection Method for the Incompressible Navier-Stokes Equations,' J, Comput. Phys., Vol. 85, pp. 257-283
  3. Choi, H. and Moin, P., 1994, 'Effects of the Computational Time Step on Numerical Solutions of Turbulent Flow,' J. Comput. Phys., Vol. 114, pp. 1-4
  4. Choi, H., Moin, P. and Kim, J., 1993, 'Direct Numerical Simulation of Turbulent Flow over Riblets,' J. Fluid Mech., Vol. 255, pp. 503-539
  5. Chorin, A. J., 1968, 'Numerical Solution of the Navier-Stokes Equations,' Math.Comput., Vol. 22, pp. 745-762
  6. Dukowicz, J. and Dvinsky, A., 1992, Approximate Factorization as a High Order Splitting for the Implicit Incompressible Flow Equations,' J. Comput. Phys., Vol. 102, pp. 336-347
  7. Hahn, S. and Choi, H., 1997, 'Unsteady Simulation of Jets in a Cross Flow,' J. Comput. Phys., Vol. 134, pp. 342-356
  8. Jimenez, J. and Moin, P., 1991, 'The Minimal Flow Unit in Near-Wall Turbulence,' J. Fluid Mech., Vol. 225, pp. 213-240
  9. Kim, J. and Moin, P., 1985, 'Application of a Fractional Step Method to Incompressible Navier-Stokes Equations,' Journal of Computational Physics, Vol. 59, pp. 308-323
  10. Le, H. and Moin, P., 1991, An Improvement of Fractional Step Methods for the Incompressible Navier-Stokes Equations,' J. Comput. Phys., Vol. 92, pp. 369-379
  11. Perot, J., 1993, 'An Analysis of Fractional Step Method,' J. Comput. Phys., Vol. 108, pp. 51-58
  12. Rosenfeld, M., 1996, 'Uncoupled Temporally Second-order Accurate Implicit Solver of Incompressible Navier-Stokes Equations,' AIAA J., Vol. 34, No. 9, pp. 1829-1834
  13. Temam, R., 1979, Navier-Stokes Equations ; Theory and Numerical Analysis, North-Holland, New York
  14. Van Kan, J., 1986, A Second-Order Accurate Pressure Correction Scheme for Viscous Incompressible Flow,' SIAM J. Sci. Stat. Comput., Vol. 7, p. 870
  15. You, J., Choi, H. and You, J. Y, 1999, 'Modified fractional step method of keeping a constant mass flow rate in channel and pipe flows,' Submitted to KSME Int. J.
  16. 김동주, 최해천 1999, '비정형 격자계에서 비정상 비압축성 유동장 해석을 위한 유한체적법', 대한기계학회 1999년도 춘계학술대회논문집 B, pp. 315-320