Design of an unconditionally stable, positive scheme for the k-∈ and two-layer turbulence models

Computers and Fluids

Volumn 26, Issue 5, 1997, Pages 469-487

  Jongen, T ^a   Marx, Y P ^a  

^a EPFL   (Switzerland)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTER SIMULATION; NUMERICAL ANALYSIS; TURBULENCE;

INCOMPRESSIBLE FLOW;

TURBULENT FLOW;

MODELLING-MATHEMATICAL; TURBULENCE;

EID: 0031171877     PISSN: 00457930     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0045-7930(97)00003-0     Document Type: Article

References (22)

1. Cardot, B., Mohammadi, B. and Pironneau, O., A few tools for turbulence models in Navier-Stokes equations. In Incompressible Computational Fluid Dynamics: Trends and Advances, ed. M. Gunzburger and R. Nicolaides. Cambridge University Press, Cambridge, 1993, pp. 1-15.
2. Lien, F. S. and Leschziner, M. A., Approximation of turbulence convection in complex flows with a TVD-MUSCL scheme. Proc. 5th. Int. Symp. on Refined Flow Modelling and Turbulence Measurements, Paris, September 7-10, 1993.
3. Almeida, G. P., Durao, D. F. and Heitor, M. V., Wake flows behind two-dimensional model hills. Experimental and Thermal Fluid Science, 1993, 7, 87-101.
4. Harten, A., High resolution schemes for hyperbolic conservation laws. Journal of Computational Physics, 1983, 49, 357-393.
5. Sweby, P. K., High resolution schemes using flux limiters for hyperbolic conservation laws. SIAM Journal of Numeral Analysis, 1984, 21, 995-1011.
6. Hundsdorfer, W., Koren, B., van Loon, M. and Verwer, J., A positive finite-difference advection scheme. Journal of Computational Physics, 1995, 117, 35-46.
7. Yee, H. C., Warming, R. F. and Harten, A., Implicit total variation diminishing (TVD) schemes for steady-state calculations. Journal of Computational Physics, 1985, 57, 327-360.
8. Larrouturou, B., How to preserve mass fractions positivity when computing compressible multi-component flows. Journal of Computational Physics, 1991, 95, 59-84.
9. Chen, H. C. and Patel, V. C., Near-wall turbulence models for complex flows including separation. AIAA Journal, 1988, 6, 641-648.
10. Rodi, W., Experience with two-layer turbulence models combining the k-∈ model with a one-equation model near the wall. AIAA Paper, 91-0216, 1991.
11. Lien, F. S. and Leschziner, M. A., Computational modelling of 3D turbulent flow in S-diffuser and transition ducts. In Engineering Turbulence Modelling and Experiments 2, ed. W. Rodi and F. Martelli. Elsevier Science, 1993, pp. 217-228.
12. Wolfshtein, M., The velocity and temperature distribution in one-dimensional flow with turbulence augmentation and pressure gradient. International Journal of Heat and Mass Transfer, 1969, 12, 301-318.
13. van Leer, B., Towards the ultimate conservative difference scheme V. A second order sequel to Godunov's method. Journal of Computational Physics, 1979, 32, 101-136.
14. Spekreijse, S., Multigrid solution of monotone second-order discretizations of hyperbolic conservation laws. Mathematics and Computers, 1987, 49, 135-155.
15. Varga, R. S., Matrix Iterative Analysis. Prentice-Hall, Englewood Cliffs, NJ, 1962.
16. Patankar, S. V., Numerical Heat Transfer and Fluid Flow. Hemisphere, Washington, DC, 1980.
17. van der Vorst, H. Bi-cgstab, a fast and smoothly converging variant of bi-cg for the solution of non-symmetric linear systems. SIAM Journal of Scientific and Statistical Computing, 1992, 16, 631-644.
18. Vuik, C., Solution of the discretized incompressible Navier-Stokes equations with the GMRES method. International Journal of Numerical Methods and Fluids, 1993, 16, 507-523.
19. Chien, K. Y., Predictions of channel and boundary-layer flows with a low-Reynolds number turbulence model. AIAA Journal, 1982, 20, 33-38.
20. Marx, Y. P., Time-integration schemes for the unsteady incompressible Navier-Stokes equations. Journal of Computational Physics, 1994, 112, 182-209.
21. Reneau, L. R., Johnston, J. P. and Kline, S. J., Performance and design of straight, two-dimensional diffusers. Transactions of the ASME, Journal of Basic Engineering, 1967, 5, 141-149.
22. Baldwin, B. and Lomax, H., Thin-layer approximation and algebraic model for separated turbulent flows. AIAA Paper. 78-257, 1978.