Numerical solution of the incompressible three-dimensional Navier-Stokes equations

作者: V. Babu , Seppo A. Korpela

DOI: 10.1016/0045-7930(94)90009-4

关键词: MathematicsComputational fluid dynamicsMathematical analysisNavier–Stokes equationsAlternating direction implicit methodNumerical analysisBoussinesq approximation (water waves)Convective heat transferClassical mechanicsCompressibilityIncompressible flow

摘要: Abstract A numerical method to solve the incompressible, 3-D Navier-Stokes and Boussinesq equations in primitive variable form on non-staggered, uniform non-uniform grids, is discussed. The Neumann-Poisson problem for pressure solved by using a fast direct velocity temperature fields are advanced time with Douglas-Gunn ADI method. Accurate transient solutions 2-D convective flow shallow box heated from side have been obtained compared available results. Some results lid-driven cavity also presented.

参考文章(28)
Jim Douglas, James E. Gunn, A general formulation of alternating direction methods Numerische Mathematik. ,vol. 6, pp. 428- 453 ,(1964) , 10.1007/BF01386093
W. Roger Briley, Numerical method for predicting three-dimensional steady viscous flow in ducts Journal of Computational Physics. ,vol. 14, pp. 8- 28 ,(1974) , 10.1016/0021-9991(74)90002-3
John B Bell, Phillip Colella, Harland M Glaz, A second-order projection method for the incompressible navier-stokes equations Journal of Computational Physics. ,vol. 85, pp. 257- 283 ,(1989) , 10.1016/0021-9991(89)90151-4
Francis H. Harlow, J. Eddie Welch, Numerical Calculation of Time‐Dependent Viscous Incompressible Flow of Fluid with Free Surface Physics of Fluids. ,vol. 8, pp. 2182- 2189 ,(1965) , 10.1063/1.1761178
V. Babu, Seppo A. Korpela, Three-dimensional thermocapillary convection in a cavity Computers & Fluids. ,vol. 18, pp. 229- 238 ,(1990) , 10.1016/0045-7930(90)90022-P
Hwar C Ku, Richard S Hirsh, Thomas D Taylor, A Pseudospectral method for solution of the three-dimensional incompressible Navier-Stokes equations Journal of Computational Physics. ,vol. 70, pp. 439- 462 ,(1987) , 10.1016/0021-9991(87)90190-2
F. Sotiropoulos, S. Abdallah, Coupled fully implicit solution procedure for the steady incompressible Navier-Stokes equations Journal of Computational Physics. ,vol. 87, pp. 328- 348 ,(1990) , 10.1016/0021-9991(90)90256-Z
Reima Iwatsu, Katsuya Ishii, Tetuya Kawamura, Kunio Kuwahara, Jae Min Hyun, Numerical simulation of three-dimensional flow structure in a driven cavity Fluid Dynamics Research. ,vol. 5, pp. 173- 189 ,(1989) , 10.1016/0169-5983(89)90020-8