Comparison of Several Spatial Discretizations for the Navier-Stokes Equations

Journal of Computational Physics

Volumn 160, Issue 2, 2000, Pages 683-704

  Zingg, D W ^a   De Rango, S ^a   Nemec, M ^a   Pulliam, T H ^b  

^a UNIVERSITY OF TORONTO   (Canada)

^b NASA AMES RESEARCH CENTER   (United States)

Author keywords

Aerodynamics; Finite difference methods; Higher order methods; Navier Stokes equations

Indexed keywords

DRAG; FINITE DIFFERENCE METHOD; SUPERSONIC AIRCRAFT; TRANSONIC AERODYNAMICS; VISCOUS FLOW;

DISCRETIZATIONS; FINITE-DIFFERENCE METHODS; HIGH-ORDER METHODS; HIGHER-ORDER METHODS; MATRIX; NAVIER-STOKES EQUATION; NUMERICAL DISSIPATION; SECOND ORDERS; SPATIAL DISCRETIZATIONS; THIRD ORDER;

NAVIER STOKES EQUATIONS;

EID: 0001457781     PISSN: 00219991     EISSN: None     Source Type: Journal    
DOI: 10.1006/jcph.2000.6482     Document Type: Article

References (28)

1. S. R. Allmaras, Contamination of laminar boundary layers by artificial dissipation in Navier-Stokes solutions, in, Numerical Methods for Fluid Dynamics, edited by, M. J. Baines and K. W. Morton, Clarendon, Oxford, UK, 1993.
2. Baldwin B. S., Lomax H. Thin Layer Approximation and Algebraic Model for Separated Turbulent Flows. 1978.
3. T. J. Barth, Aspects of Unstructured Grids and Finite-Volume Solvers for the Euler and Navier-Stokes Equations, Lecture Notes, Von Karman Institute for Fluid Dynamics Lecture Series, 1994-05, Brussels, 1994.
4. Beam R., Warming R. F. An implicit finite-difference algorithm for hyperbolic systems in conservation law form. J. Comput. Phys. 22:1976;87.
5. Cook P. H., MacDonald M. A., Firmin M. C. P. Aerofoil RAE 2822 - Pressure Distributions, and Boundary-Layer and Wake Measurements. May 1979.
6. De Rango S., Zingg D. W. Aerodynamic Computations Using a Higher-Order Algorithm. January 1999.
7. Frew K., Zingg D. W., De Rango S. Artificial dissipation schemes for viscous airfoil computations. AIAA J. 36:1998;1732.
8. Gregory N., O'Reilly C. L. Low-Speed Aerodynamic Characteristics of NACA 0012 Airfoil Section, Including the Effects of Upper-Surface Roughness Simulating Hoar Frost. January 1970.
9. Holst T. L. Viscous Transonic Airfoil Workshop Compendium of Results. June 1987.
10. Jameson A. Analysis and design of numerical schemes for gas dynamics. I. Artificial diffusion, upwind biasing, limiters and their effect on accuracy and multigrid convergence. Int. J. Comput. Fluid Dynam. 4:1995;171.
11. Jameson A. Analysis and design of numerical schemes for gas dynamics. II. Artificial diffusion and discrete shock structure. Int. J. Comput. Fluid Dynam. 5:1995;1.
12. Jameson A., Schmidt W., Turkel E. Numerical Solutions of the Euler Equations by Finite Volume Methods Using Runge-Kutta Time Stepping. June 1981.
13. Jespersen D., Pulliam T., Buning P. Recent Enhancements to OVERFLOW. January 1997.
14. Klopfer G. H., Van der Wijngaart R. F., Hung C. M. A Diagonalized Diagonal Dominant Alternating Direction Implicit (D3ADI) Scheme and Subiteration Correction. 1998.
15. B. Koren, Upwind schemes, multigrid and defect correction for the steady Navier-Stokes equations, in, Proc. 2nd Int. Conf. on Nonlinear Hyperbolic Problems, edited by, J. Ballman and R. Jeltsch, Vieweg, Braunschweig, 1988.
16. B. Koren, Upwind schemes for the Navier-Stokes equations, in, Proc. 11th Int. Conf. on Num. Meth. in Fluid Dynamics, edited by, D. L. Dwoyer, M. Y. Hussaini, and R. G. Voigt, Springer-Verlag, Berlin, 1989.
17. Maksymiuk C. M., Swanson R. C., Pulliam T. H. A Comparison of Two Central Difference Schemes for Solving the Navier-Stokes Equations. July 1990.
18. Nemec M., Zingg D. W. Aerodynamic computations using the convective upstream split pressure scheme with local preconditioning. AIAA J. 38:2000.
19. Pulliam T. H. Lecture Notes, Von Karman Institute for Fluid Dynamics Lecture Series. Efficient Solution Methods for the Navier-Stokes Equations. 1986.
20. Pulliam T. H., Chaussee D. S. A diagonal form of an implicit approximate-factorization algorithm. J. Comput. Phys. 39:1981;347.
21. Roache P. J. Verification and Validation in Computational Science and Engineering. 1998.
22. Roe P. L. Approximate Riemann solvers, parameter vectors, and difference schemes. J. Comput. Phys. 43:1981;357.
23. Swanson R. C., Turkel E. On central-difference and upwind schemes. J. Comput. Phys. 101:1992;292.
24. Swanson R. C., Radespiel R., Turkel E. On some numerical dissipation schemes. J. Comput. Phys. 147:1998;518.
25. Tatsumi S., Martinelli L., Jameson A. A New High Resolution Scheme for Compressible Viscous Flow with Shocks. January 1995.
26. Van Albada G. D., Van Leer B., Roberts W. W. A comparative study of computational methods in cosmic gas dynamics. Astron. Astrophys. 108:1982;76.
27. Venkatakrishnan V. Convergence to steady state solutions of the Euler equations on unstructured grids with limiters. J. Comput. Phys. 118:1995;120.
28. Zingg D. W. Grid studies for thin-layer Navier-Stokes computations of airfoil flowfields. AIAA J. 30:1992;2561.