A novel implicit difference algorithm of primitive variable flow equations with higher-order extra terms

Computers and Fluids

Volumn 26, Issue 2, 1997, Pages 163-182

  Ng, E Y K ^a   Liu, S Z ^b  

^a NANYANG TECHNOLOGICAL UNIVERSITY   (Singapore)

^b DSO NATIONAL LABORATORIES   (Singapore)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; CASCADES (FLUID MECHANICS); COMPUTATIONAL GEOMETRY; COMPUTATIONAL METHODS; CONVERGENCE OF NUMERICAL METHODS; EQUATIONS OF MOTION; MATHEMATICAL TRANSFORMATIONS; NAVIER STOKES EQUATIONS; ROTORS; SHOCK WAVES; STATORS; TRANSONIC FLOW;

BEAM WARMING SCHEME; FLOW EQUATIONS; FLUX VECTOR SPLITTING METHOD; STEGER IMPLICIT FACTORED SCHEME;

COMPUTATIONAL FLUID DYNAMICS;

COMPUTATIONAL FLUID DYNAMICS; EULER FLOW; NAVIER-STOKES EQUATIONS;

EID: 0031079623     PISSN: 00457930     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0045-7930(96)00036-9     Document Type: Article

References (25)

1. Beam, R. M. and Warming, R. F., An implicit finite-difference algorithm for hyperbolic systems in conservation-law form. J. Computat. Phys., 1976, 22, 87-110.
2. MacCormack, R. W., An efficient numerical method for solving the time-dependent compressible Navier-Stokes equations at high Reynolds number. NASA TM X-73, July 1976, p. 129.
3. Thomas, J. L. and Walters, R. W., Upwind relaxation algorithms for the Navier-Stokes equations. Proc. AIAA 7th Computational Fluid Dynamics Conf., Paper 85-1501, June 1985.
4. Beam, R. M. and Warming, R. F., An implicit factored scheme for the compressible Navier-Strokes equations. AIAA J., 1978, 16, 4, 393-402.
5. Steger, J. L., Coefficient matrices for implicit finite difference solution of the inviscid fluid conservation law equations. Computer Meth. in Appl. Mech. and Engng, 1978, 13, 175.
6. Steger, J. L. and Warming, R. F., Flux vector splitting of the inviscid gasdynamics equation with application to finite difference methods. J. Computat. Phys., 1981, 40, 2, 263-293.
7. Chakravarthy, S. R., Anderson, D. A. and Salas, M. D., The split coefficient matrix method for hyperbolic systems of gasdynamics equations. AIAA Paper 80-0268, 1980.
8. Moretti, G., An old integration scheme for compressible flows revisited. Refurbished and put to work. Computat. Fluids, 1979, 7, 191.
9. Anderson, W. K., Thomas, J. L. and David, L. W., Multigrid acceleration of the flux split Euler equations. AIAA J., 1988, 26, 6, 649-654.
10. Taylor, A. C., Ng, W. and Walters, R., An improved upwind finite volume relaxation method for high speed viscous flows. AIAA Paper 89-0549, 1989.
11. Van Leer, B., Flux-vector splitting for the Euler equations. Lecture Notes in Physics, 1982, 170, Springer-Verlag, p. 507.
12. MacCormack, R. W., A numerical method for solving the equations of compressible viscous flow. AIAA Paper 81-0110, 1981.
13. Von Lavante, E. and Lyer, V. S. V., Simplified implicit block-bidiagonal finite difference method for solving the Navier-Strokes equations. AIAA J., 1985, 23, 7, 1130-1132.
14. Dawes, W. N., A pre-processed implicit algorithm for 3D viscous compressible flow. In Notes on Numerical Fluid Mechanics, Vol. 12. Vieweg, 1986, pp. 70-77.
15. Jameson, A., Successes and challenges in computational aerodynamics. Proc. AIAA 8th CFD Conf., 1987. AIAA, 1-35.
16. Sankar, N. L., Malone, J. B. and Tassa, Y., An implicit conservative algorithm for steady and unsteady three-dimensional potential flows. AIAA Paper 81-1016, 1981.
17. Ames, W. F., Numerical Methods for Partial Differential Equations, 2nd edn. Academic, New York, 1977.
18. Anderson, D. A., Tannehill J. C. and Pletcher R. H., Computational Fluid Mechanics and Heat Transfer. Hemisphere Publishing Corporation, New York, 1984.
19. Hedstrom, G. W., Nonreflecting boundary conditions for nonlinear hyperbolic systems. J. Computat. Phys., 1979, 32.
20. Liu, J. M., Liu, B. and Xiang, Y. M., An explicit-implicit numerical method for 3-D compressible N-S equations. Proc. 4th Int. Symposium on Transport Phenomena and Dynamics of Rotating Machinery, Honolulu, 1992, pp. 544-552.
21. Baldwin, B. S. and Lomax, H., Thin layer approximation and algebraic model for separated turbulent flows. AIAA Paper 78-257, 1978.
22. Zheng, Z., Transonic flow calculation for two-dimensional nozzle. J. Aerodynamics, 1989, 7, 4.
23. Zhang, Y., Gong, Z. and Sheng, M., On the solution of transonic flow of plane cascade by a time-marching method. J. Thermophy. Engng, 1980, 1, 4, 337-340. P.R. China.
24. Fottner, L., Test cases for computation of internal flows in aero engine components. AGARD-AR-275, 1990.
25. Buelow, P. E. O., Venkateswaran and Merkle, C. L., Effect of grid aspect ratio on convergence. AIAA J., 1994, 32, 12, 2401-2408.