{"title":"Significance of Splitting Method in Non-linear Grid system for the Solution of Navier-Stokes Equation","authors":"M. Zamani, O. Kahar","volume":26,"journal":"International Journal of Mechanical and Mechatronics Engineering","pagesStart":149,"pagesEnd":154,"ISSN":"1307-6892","URL":"https:\/\/publications.waset.org\/pdf\/12159","abstract":"

Solution to unsteady Navier-Stokes equation by Splitting method in physical orthogonal algebraic curvilinear coordinate system, also termed 'Non-linear grid system' is presented. The linear terms in Navier-Stokes equation are solved by Crank- Nicholson method while the non-linear term is solved by the second order Adams-Bashforth method. This work is meant to bring together the advantage of Splitting method as pressure-velocity solver of higher efficiency with the advantage of consuming Non-linear grid system which produce more accurate results in relatively equal number of grid points as compared to Cartesian grid. The validation of Splitting method as a solution of Navier-Stokes equation in Nonlinear grid system is done by comparison with the benchmark results for lid driven cavity flow by Ghia and some case studies including Backward Facing Step Flow Problem.<\/p>\r\n","references":" G. Karniadakis, M. Israeli, and S. Orszag, 1991, \"High-order splitting\r\nmethods for the incompressible Navier-Stokes equations,\" Journal of\r\nComputational Physics, 97, pp, 414-443.\r\n U. Ghia, K. N. Ghia and C. T. Shin, 1982, \"High-Re Solutions for\r\nIncompressible Flow Using the Navier-Stokes Equations and a Multigrid\r\nMethod,\" Journal of Computational Physics, 48, 387-411.\r\n J. C. Tannehill, D. A. Anderson, R. H. Pletcher, 1997, Computational\r\nFluid Mechanics and Heat Transfer. Taylor and Francis Publisher, New\r\nYork.\r\n S. K. Choi, H. Y. Nam, Y. B. Lee and M. Cho (1993), \"An Efficient\r\nThree-Dimensional Calculation Procedure for Incompressible Flows in\r\nComplex Geometries\", Numerical Heat Transfer, Part B, 23, 387-400.\r\n I. Demirdzic and M. Peric (1990), \"Finite Volume Method for Prediction\r\nof Fluid Flow in Arbitrary Shaped Domains with Moving Boundaries\",\r\nInternational Journal for Numerical Methods in Fluids, 10, 771-790.\r\n P. N. Childs, J. A. Shaw, A. J. Peace and J. M. Georgala (1992),\r\n\"SAUNA: A System for Grid Generation and Flow Simulation using\r\nhybrid\/Structured\/Unstructured Grids\", in Computational Fluid\r\nDynamics,Proceedings of the 1st European CFD Conference, Volume 2,\r\n875-882.\r\n S. V. Patankar (1980), Numerical Heat Transfer and Fluid Flow.\r\nMcGraw-Hill, New York.\r\n R. Courant, E. Isaacson and M. Rees (1952), \"On the Solution of\r\nNonlinear Hyperbolic Differential Equations by Finite Difference\",\r\nCommunications in Pure and Applied Mathematics, 5, 243-255.\r\n D. B. Spalding (1972), \"A Novel Finite Difference Formulation for\r\nDifferential Expressions Involving both First and Second Derivatives\",\r\nInternational Journal for Numerical Methods in Engineering, 4, 551-\r\n559.\r\n S. V. Patankar (1979), \"A Calculation Procedure for Two Dimensional\r\nElliptic Situations\", Numerical Heat Transfer, 2.\r\n O. Kahar (2004), \"Multiple Steady solutions and bifurcations in the\r\nSymmetric Driven Cavity\"., Universiti Teknologi Malaysia.","publisher":"World Academy of Science, Engineering and Technology","index":"Open Science Index 26, 2009"}