References

 

[1]
Anderson DA, Tannehill JC, Pletcher RH, 1984. Computational Fluid Mechanics and Heat Transfer. McGraw-Hill, New York.

[2]
Barragy E, Carey GF, 1997. Stream function-vorticity driven cavity solutions using p finite elements. Computers and Fluids 26, 453- 468.

[3]
Botella O, Peyret R, 1998. Benchmark spectral results on the lid-driven cavity flow. Computers and Fluids 27, 421- 433.

[4]
Chung TJ, 2002. Computational Fluid Dynamics. Cambridge University Press, Cambridge.

[5]
Dennis SC, Hudson JD, 1989. Compact h4 Finite Difference Approximations to Operators of Navier-Stokes Type, Journal of Computational Physics 85, 390-416.

[6]
Erturk E, Corke TC, Gokcol C, 2005. Numerical Solutions of 2-D Steady Incompressible Driven Cavity Flow at High Reynolds Numbers, International Journal for Numerical Methods in Fluids 48, 747-774.

[7]
Erturk E, Gokcol C, 2006. Fourth Order Compact Formulation of Navier-Stokes Equations and Driven Cavity Flow at High Reynolds Numbers, International Journal for Numerical Methods in Fluids 50, 421-436.

[8]
Erturk E, 2008. Numerical Performance of Compact Fourth-Order Formulation of the Navier-Stokes Equations, Communications in Numerical Methods in Engineering, In Press, DOI: 10.1002/cnm.1090.

[9]
Ge L, Zhang J, 2001. High Accuracy Iterative Solution of Convection Diffusion Equation with Boundary Layers on Nonuniform Grids, Journal of Computational Physics 171, 560-578.

[10]
Gresho PM, 1991. Incompressible Fluid Dynamics: Some Fundamental Formulation Issues, Annual Review of Fluid Mechanics 23, 413-453

[11]
Gupta MM, Manohar RP, Stephenson JW, 1984. A Single Cell High Order Scheme for the Convection-Diffusion Equation with Variable Coefficients, International Journal for Numerical Methods in Fluids 4, 641-651.

[12]
Huang H, Yang H, 1990. The Computational Boundary Method for Solving the Navier-Stokes Equations, Institute of Applied Mathematics and Statistics Technical Report. No: Iam90-05, http://www.iam.ubc.ca/pub/techreports/.

[13]
Lele SK, 1992. Compact finite difference schemes with spectral-like resolution, Journal of Computational Physics 103, 16-42.

[14]
Li M, Tang T, Fornberg B, 1995. A Compact Forth-Order Finite Difference Scheme for the Steady Incompressible Navier-Stokes Equations, International Journal for Numerical Methods in Fluids 20, 1137-1151.

[15]
MacKinnon RJ, Johnson RW, 1991. Differential-Equation-Based Representation of Truncation Errors for Accurate Numerical Simulation, International Journal for Numerical Methods in Fluids 13, 739-757.

[16]
Peaceman DW, Rachford Jr. HH, 1955. The numerical solution of parabolic and elliptic differential equations, Journal of the Society for Industrial and Applied Mathematics 3, 28-41.

[17]
Richards CW, Crane CM, 1979. The accuracy of finite difference schemes for the numerical solution of the Navier-Stokes equations, Applied Mathematical Modelling 3, 205-211.

[18]
Schreiber R, Keller HB, 1983. Driven cavity flows by efficient numerical techniques. Journal of Computational Physics 49, 310 -333.

[19]
Spotz WF, Carey GF, 1995. High-Order Compact Scheme for the Steady Streamfunction Vorticity Equations, International Journal for Numerical Methods in Engineering 38, 3497-3512.

[20]
Spotz WF, Carey GF, 1998. Formulation and Experiments with High-Order Compact Schemes for Nonuniform Grids, International Journal of Numerical Methods for Heat and Fluid Flow 8, 288-303.

[21]
Spotz WF, 1998. Accuracy and Performance of Numerical Wall Boundary Conditions For Steady, 2D, Incompressible Streamfunction Vorticity, International Journal for Numerical Methods in Fluids 28, 737-757.

[22]
Stortkuhl T, Zenger C, Zimmer S, 1994. An Asymptotic Solution for the Singularity at the Angular Point of the Lid Driven Cavity, International Journal of Numerical Methods for Heat and Fluid Flow 4, 47-59.

[23]
Visbal MR, Gaitonde DV, 1999. High-Order-Accurate Methods for Complex Unsteady Subsonic Flows, AIAA Journal 37, 1231-1239.

[24]
Yang HH, 1993. The Computational Boundary Method for Solving the Incompressible Flows, Applied Mathematics Letters 6, 3-7.

[25]
Zhang J, 1998. An Explicit Fourth-Order Compact Finite Difference Scheme for Three-Dimensional Convection-Diffusion Equation, Communications in Numerical Methods in Engineering 14, 209-218.

[26]
Zingg DW, 1996. On finite-difference methods for linear acoustic wave propagation, AIAA Paper, Paper No:1996-280.

[27]
Zingg DW, 2000. Comparison of High-Accuracy Finite-Difference Methods for Linear Wave Propagation, SIAM Journal on Scientific Computing 22, 476-502.