zbMATH — the first resource for mathematics

Computational method for turbulent supersonic flows. (Russian, English) Zbl 1212.65262
Mat. Model. 21, No. 12, 103-121 (2009); translation in Math. Models Comput. Simul. 2, No. 4, 407-422 (2010).
A variant of Godunov’s method of higher order of accuracy is proposed. The variant is more suitable for the numerical analysis of compressible turbulent flows on a base of semi-empiric turbulence models.

65Lxx Numerical methods for ordinary differential equations
65L06 Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations
76J20 Supersonic flows
Full Text: DOI
[1] Launder, B. E.; Spalding, D. B., The Numerical Computation of Turbulent Flows, Comp. Meth. Appl. Mech. Engn., 3, 3, 269-289 (1974) · Zbl 0277.76049
[2] Glushko, G. S.; Ivanov, I. E.; Kryukov, I. A., The Computation of Supersonic Turbulence Flows (2006), Moscow: IPM RAN, Moscow
[3] Harten, A., High Resolution Schemes for Hyperbolic Conservation Laws, J. Comp. Phys., 49, 357-393 (1983) · Zbl 0565.65050
[4] Harten, A.; Engguist, B.; Osher, S.; Chakravarthy, S. R., Uniformly High Order Accurate Essentially Non-Oscillatory Schemes, III, J. Comp. Phys., 71, 231-303 (1987) · Zbl 0652.65067
[5] Bakhvalov, N. S., Numerical Methods (1975), Moscow: Nauka, Moscow
[6] Godunov, S. K.; Zabrodin, A. V.; Ivanov, M. Ya.; Kraiko, A. N.; Prokopov, G. P., The Numerical Solution of Multidimensional Problems of Gas Dynamics (1976), Moscow: Nauka, Moscow
[7] Shu, C.-W.; Osher, S., Efficient Implementation of Essentially Non-Oscillatory Shock-Capturing Schemes, J. Comp. Phys., 77, 439-471 (1988) · Zbl 0653.65072
[8] Toro, E., Riemann Solvers and Numerical Methods for Fluid Dynamics (1999), New York: Springer-Verlag, New York
[9] H. Guillard and A. Murrona, “On the Behavior of Upwind Schemes in the Low Mach Number Limit: II. Godunov Type Schemes,” INRIA, Rapport de reserche (2001), pp. 41-89.
[10] Guillard, H.; Viozat, C., On the Behavior of Upwind Schemes in the Low Mach Number Limit, Comp. Fluids, 96, 28-63 (1999) · Zbl 0963.76062
[11] Chorin, A. J., A Numerical Method for Solving Incompressible Viscous Problems, J. Comp. Phys., 2, 2-12 (1967)
[12] Turkel, E., Preconditioned Methods for Solving the Incompressible and Low Speed Compressible Equations, J. Comp. Phys., 72, 277-298 (1987) · Zbl 0633.76069
[13] Kulikovskii, A. G.; Pogorelov, N. V.; Semenov, A. Yu., Mathematical Problems of Numerical of Hyperbolic Systems (2001), Moscow: Fizmatlit, Moscow · Zbl 0965.35001
[14] Ivanov, I. E.; Kryukov, I. A., Quasi-Monotonic Methods of High Order for Calculating the Internal and Jet Flows of Inviscid Gas, Mat. Modelir., 8, 6, 47-55 (1996) · Zbl 0993.76533
[15] Tillyaeva, N. I., Godunov’s Modified Schemes Generalization to Arbitrary Irregular Grids, Uchenye Zapiski TsAGI, XVII, 2, 18-26 (1986)
[16] Kunz, R. F.; Lakshminarayana, B., Stability of Explicit Navier-Stokes Procedures Using k-ɛ and k-ɛ/Algebraic Reynolds Stress Turbulence Models, J. Comp. Phys., 103, 141-159 (1992) · Zbl 0778.76059
[17] Gerolymos, G. A., Implicit Multiple Grid Solution of the Compressible Navier-Stokes Equations Using k-ɛ Turbulencs Closure, AIAA J., 28, 10, 1707-1717 (1990)
[18] Menter, F. R., Zonal Two-Equation k-ω Models for Aerodynamics Flow, AIAA Pap., 93, 2906 (1993)
[19] Kral, L. D.; Mani, M.; Ladd, J. A., Application of Turbulence Models for Aerodynamic and Propulsion Flowfields, AIAA J., 34, 11, 2291-2298 (1996) · Zbl 0900.76163
[20] S. B. Pope, Turbulent Flows (Cambridge Univ. Press, 2000). · Zbl 0966.76002
[21] Park, C. H.; Park, S. O., On the Limits of Two-Equation Turbulence Models, Int. J. CFD, 19, 1, 79-86 (2005) · Zbl 1286.76071
[22] Liu, F.; Zeng, X., A Strongly Coupled Time-Marching Method for Solving the Navier-Stokes and k-ω Turbulence Model Equations with Multigrid, J. Comp. Phys., 128, 2, 289-300 (1996) · Zbl 0862.76064
[23] Ilinca, F.; Peiletier, D., Positivity Preservation and Adaptive Solution for the k-ɛ Model of Turbulence, AIAA Pap., 97, 0205 (1997)
[24] G. L. Vasil’tsov, G. S. Glushko, and I. A. Kryukov, “The Calculation of Turbulent Flows for the Areas of Complicated Geometry,” Preprint no. 608 IPMech RAS (IPMekh RAN, 1998).
[25] S.-E. Kim and D. Choudhury, “A Near-Wall Treatment Using Wall Functions Sensitized to Pressure Gradient, Separated and Complex Flows,” ASME FED 217 (1995).
[26] White, F. M., Viscous Fluid Flow (1974), New York: McGraw-Hill, New York · Zbl 0356.76003
[27] J. M. Seiner and T. D. Norum, “Experiments of Shock Associated Noise on Supersonic Jets,” AIAA Pap. 79-1526 (1979).
[28] C. A. Hunter, “Experimental, Theoretical, and Computational Investigation of Separated Nozzle Flows,” AIAA Pap. 98-3107 (1998).
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.