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On the accuracy and efficiency of CFD methods in real gas hypersonics. (English) Zbl 0772.76046

Summary: A study of viscous and inviscid hypersonic flows using generalized upwind methods is presented. A new family of hybrid flux-splitting methods is examined for hypersonic flows. The hybrid method is constructed by the superposition of the flux-vector-splitting method and second-order artificial dissipation in the regions of strong shock waves. The conservative variables on the cell faces are calculated by an upwind extrapolation scheme to third-order accuracy. A second-order-accurate scheme is used for the discretization of the viscous terms. The solution of the system of equations is achieved by an implicit unfactored method. In order to reduce the computational time, a local adaptive mesh solution (LAMS) method is proposed. The LAMS method combines the mesh-sequencing technique and local solution of the equations. The local solution of either of Euler or the Navier-Stokes equations is applied for the region of the flow field where numerical disturbances die out slowly. Validation of the Euler and Navier-Stokes codes is obtained for hypersonic flows around blunt bodies. Real gas effects are introduced via a generalized equation of state.

MSC:

76M20 Finite difference methods applied to problems in fluid mechanics
76K05 Hypersonic flows
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[1] and , Hypersonic Flow Theory, Academic, New York, 1959. · Zbl 0084.42202
[2] Hypersonic and High Temperature Gas Dynamics, McGraw-Hill, New York, 1982.
[3] Steger, J. Comput. Phys. 40 pp 263– (1981)
[4] Roe, J. Comput. Phys. 43 pp 357– (1981)
[5] van Leer, J. Comput. Phys. 14 pp 361– (1974)
[6] ’Upwind and symmetric shock capturing schemes’, NASA-TM 89464, 1987.
[7] ’High resolution upwind formulations for the Navier-Stokes equations’, VKI Lecture Ser., Comput. Fluid Dyn., 1988-05, 1988.
[8] MacCormack, Comput. Fluids 17 pp 135– (1989)
[9] ’Computational techniques for hypersonic flows’, AGARD 761, 1988.
[10] and , ’Generalized flux vectors for hypersonic shock capturing’, AIAA Paper 90-0390, 28th Aerospace Science Meeting, Reno, NV, 1990.
[11] ’Simple improvements of an upwind scheme for hypersonic flows’, AIAA Paper 89-1977, 9th CFD Conf., Buffalo, NY, 1989.
[12] ’Characteristic flux averaging approach to the solution of the Euler’s equations’, VKI Lecture Ser., Comput. Fluid Dyn., 1987-04, 1987.
[13] Anderson, AIAA J. 24 pp 1453– (1986)
[14] , and , ’Application of a new class of high accuracy TVD schemes to the Navier-Stokes equations’, AIAA Paper 85-0165, 1985.
[15] ’Relaxation methods for unfactored implicit upwind schemes’, AIAA Paper 84-0165, 22nd Aerospace Sciences Meeting, Reno, NV, 1984.
[16] and , ’Verification of an implicit relaxation method for steady and unsteady viscous and inviscid flow problems’, AGARD CP-437, 1988, pp. 15-1-15-33.
[17] Drikakis, AIAA J. 30 pp 340– (1992)
[18] Colella, J. Comput. Phys. 87 pp 171– (1990)
[19] and , ’Laminar and turbulent viscous compressible flows using improved flux vector splittings’, in and (eds), Proc. 9th GAMM Conf. on Numerical Methods in Fluid Mechanics, Notes on Numerical Fluid Mechanics, Vol.35, Vieweg, Braunschweig, 1992, pp. 407-416. · Zbl 0761.76050 · doi:10.1007/978-3-663-13974-4_39
[20] ’Development of upwind numerical methods for high speed aerodynamics’, Ph.D. Dissertation, National Technical University of Athens, 1991.
[21] and , ’On the accuracy of upwind schemes for the solution of the Navier-Stokes Equations’, AIAA Paper 87-1105, 8th CFD Conf., Honolulu, HW, 1987.
[22] , and , ’A comparison of numerical flux formulas for the Euler and Navier-Stokes equations’, AIAA Paper 87-1104, 8th CFD Conf., Honolulu, HW, 1987.
[23] ’Efficient solution methods for the Navier-Stokes equations’, VKI Lecture Ser., 1986.
[24] Panaras, J. Comput. Phys. 82 pp 429– (1989)
[25] Grossman, Comput. Fluids 17 pp 99– (1989)
[26] Liou, J. Comput. Phys. 87 pp 1– (1990)
[27] Glaister, J. Comput. Phys. 77 pp 361– (1988)
[28] Drikakis, Int. j. numer. methods fluids 12 pp 711– (1991)
[29] and , ’Simplified curve fits for the transport properties of equilibrium air’, NASA CR-178411, 1987.
[30] and , ’Simplified curve fits for the thermodynamic properties of the equilibirum air’, NASA RP-1181, 1987.
[31] Grossman, AIAA J. 27 pp 524– (1989)
[32] Billig, J. Spacecr. Rockets 4 pp 822– (1967)
[33] ’Hypersonic three-dimensional Navier-Stokes calculations for equilibrium gas’, AIAA Paper 89-2183, 7th Applied Aerodynamics Conf., Seattle, WA, 1989.
[34] and , ’Calculation of viscous hypersonic flows using a coupled Euler/2nd order boundary layer method’, MBB-FE122-S-PUB-387, 1989.
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