An implicit numerical scheme for solution of incompressible Navier-Stokes equations on curvilinear grids
0
조회
0
다운로드
0
인용
0
참고문헌
키워드
초록
This article deals with implementation of a high-order finite difference scheme for numerical solution of the incompressible Navier-Stokes equations on curvilinear grids. The numerical scheme is based on pseudo-compressibility approach. A fifth-order upwind compact scheme is used to approximate the inviscid fluxes while the discretization of metric and viscous terms is accomplished using sixth-order central compact scheme. An implicit Euler method is used for discretization of the pseudo-time derivative to obtain the steady-state solution. The resulting block tridiagonal matrix system is solved by approximate factorization based alternating direction implicit scheme (AF-ADI) which consists of an alternate sweep in each direction for every pseudo-time step. The convergence and efficiency of the method are evaluated by solving some 2D benchmark problems. Finally, computed results are compared with numerical results in the literature and a good agreement is observed.
Abstract
This article deals with implementation of a high-order finite difference scheme for numerical solution of the incompressible Navier-Stokes equations on curvilinear grids. The numerical scheme is based on pseudo-compressibility approach. A fifth-order upwind compact scheme is used to approximate the inviscid fluxes while the discretization of metric and viscous terms is accomplished using sixth-order central compact scheme. An implicit Euler method is used for discretization of the pseudo-time derivative to obtain the steady-state solution. The resulting block tridiagonal matrix system is solved by approximate factorization based alternating direction implicit scheme (AF-ADI) which consists of an alternate sweep in each direction for every pseudo-time step. The convergence and efficiency of the method are evaluated by solving some 2D benchmark problems. Finally, computed results are compared with numerical results in the literature and a good agreement is observed.
참고문헌 (21)
- C. Azwadi, "Four sided lid-driven cavity flow using time splitting method of Adam Bashforth scheme", Int. J. of Autom and Mech. Eng. (IJAME), 9, pp.1501~1510 (2014)[DOI]
- R. Beam, "An implicit scheme for the compressible Navier-Stokes equations", AIAA J., 16, pp.393~402 (1978)[DOI]
- A. J. Chorin, "A numerical method for solving incompressible viscous flow problems", J. Comput. Phys., 2, pp.12~26 (1967)[DOI]
- J. A. Ekaterinaris, "High-order accurate numerical solutions of incompressible flows with the artificial compressibility method", Internat. J. Numer. Methods Fluids, 45(11), pp.1187~1207 (2004)[DOI]
- E. Erturk, "Numerical solution of 2D steady incompressible flow in a driven skewed cavity flow at high Reynolds numbers", Z. Angew Math. Mech., 87(5), pp.377~392 (2007)[DOI]
- H. Fadel, "High-order finite difference schemes for incompressible flows", Internat. J. Numer. Methods Fluids, 65(9), pp.1050~1070 (2011)[DOI]
- D. Fu, "A high order accurate difference scheme for complex flow fields", J. Comput. Phys., 134(1), pp.1~15 (1997)[DOI]
- D. Fu, "Nonphysical oscillations in numerical solutions: reason and improvement", CFD J., 4(4), pp.427~450 (1996)
- U. Ghia, "High Re solutions for incompressible Navier-Stokes equations", J. Comput. Phys., 49, pp.387~411 (1983)
- Low speed aerodynamic characteristics of NACA 0012 airfoil section, including the effects of upper surface roughness simulation hoarfrost, Aero Report 1308, "N. Gregory", National Physics Laboratory, ~ (1970)
- J. C. Kalita, "An efficient transient Navier-Stokes solver on compact nonuniform space grids", J. Comput. Appl. Math., 214(1), pp.148~162 (2008)[DOI]
- L. I. G. Kovasznay, "Laminar flow behind two-dimensional grid", Proc. Cambridge Philos. Soc., 44, pp.58~62 (1948)[DOI]
- S. K. Lele, "Compact finite difference schemes with spectral-like resolution", J. Comput. Phys., 103(1), pp.16~42 (1992)[DOI]
- H. Luo, "On the contravariant form of the Navier-Stokes equations in time-dependent curvilinear coordinate systems", J. Comput. Phys., 199(1), pp.355~375 (2004)[DOI]
- R. Nayak, "Numerical study of mixed convection and entropy generation of Cu-Water nano fluid in a differentially heated skewed enclosure", Int. J. Heat and Mass Transfer, 85, pp.620~634 (2015)[DOI]
- A. D. Perumal, "Simulation of incompressible flows in two-sided lid-driven square cavities. Part II - LBM", CFD Letters, 2(1), pp.25~38 (2010)
- P. L. Roe, "Approximate Riemann solvers, parameter vectors, and difference schemes", J. Comput. Phys., 43(2), pp.357~372 (1981)[DOI]
- S. E. Rogers, "An upwind differencing scheme for the incompressible Navier-Stokes equations", Appl. Numer. Math., 8(1), pp.43~64 (1991)[DOI]
- A. Shah, "A third-order upwind compact scheme on curvilinear meshes for the incompressible Navier-Stokes equations", Commun. Comput. Phys., 5(2-4), pp.712~729 (2009)
- A. Shah, "Upwind compact finite difference scheme for time-accurate solution of the incompressible Navier-Stokes equations", Appl. Math. Comput., 215(9), pp.3201~3213 (2010)
- M. R. Visbal, "On the use of higher-order finite-difference schemes on curvilinear and deforming meshes", J. Comput. Phys., 181(1), pp.155~185 (2002)[DOI]