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Methods for the accurate computations of hypersonic flows. II: Shock-aligned grid technique. (English) Zbl 1106.76422
Summary: In order to eliminate or minimize the numerical error by shock waves due to grid distribution in multidimensional hypersonic flows, a new grid reconstruction scheme, the shock-aligned grid technique (SAGT), is proposed. The error due to shock waves in a non-shock-aligned grid system magnifies in proportion to the Mach number and propagates on the downstream side of the flow field to contaminate sensitive aerodynamic coefficients or flow quantities. SAGT, combined with the AUSMPW+ scheme proposed in Part I of the present work [Zbl 1106.76422], not only provides an accurate solution but also reduces the grid dependency of a numerical scheme without a substantial increase in computational cost. In addition, SAGT is robust and flexible enough to deal with complex flow problems involving shock interaction and reflection and equilibrium and nonequilibrium effects. Extensive numerical tests from a hypersonic blunt body flow to hypersonic nonequilibrium flows validate the accuracy, efficiency, robustness, and convergence characteristics of SAGT.

MSC:
76M25 Other numerical methods (fluid mechanics) (MSC2010)
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
65M50 Mesh generation, refinement, and adaptive methods for the numerical solution of initial value and initial-boundary value problems involving PDEs
76K05 Hypersonic flows
76L05 Shock waves and blast waves in fluid mechanics
76V05 Reaction effects in flows
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[1] Lee, T.K.; Zhong, X., Spurious numerical oscillations in simulation of supersonic flows using shock-capturing schemes, Aiaa j., 37, 313, (1999)
[2] S. Srinivasan, J. C. Tannehill, and, K. J. Weilmuenster, Simplified Curve Fits for the Thermodynamic Properties of Equilibrium Air, NASA RP-1181, Aug. 1987.
[3] R. N. Gupta, K. P. Lee, R. A. Thompson, and, J. M. Yos, Calculations and Curve Fits of Thermodynamic and Transport Properties for Equilibrium Air to 30000 K, NASA RP-1260, 1991.
[4] Murthy, T.K.S., computational methods in hypersonic aerodynamics, (1991), Kluwer Academic Dordrecht · Zbl 0777.00022
[5] Park, C., Review of chemical-kinetic problems of future NASA missions, I: Earth entries, J. thermophys. heat transfer, 7, 385, (1993)
[6] R. K. Prabhu, J. R. Stewart, and, R. R. Thareja, Shock Interference Studies on a Circular Cylinder at Mach 16, Technical Paper 90-0606, AIAA Press, Washington, DC, 1990.
[7] G. H. Furumoto, and, X. Zhong, Numerical Simulation of Viscous Unsteady Type IV Shock-Shock Interaction with Thermochemical Nonequilibrium, Technical Paper 97-0982, AIAA Press, Washington, DC, 1997.
[8] K. H. Kim, C. Kim, and, O. Rho, Accurate Computations of Hypersonic Flows Using AUSMPW+ Scheme and Shock-Aligned Grid Technique, Technical Paper 98-2442, AIAA Press, Washington, DC, 1998.
[9] Kim, K.H.; Rho, O.H., An improvement of AUSM schemes by introducing the pressure-based weight functions, Comput. fluids, 27, 311, (1998) · Zbl 0964.76064
[10] Hirsh, C., numerical computation of internal and external flows, (1990), Wiley New York
[11] H. C. Yee, G. H. Kolpfer, and, J. L. Montague, High-Resolution Shock Capturing Schemes for Inviscid and Viscous Hypersonic Flows, NASA TM 101088, 1989.
[12] J. V. Rosendale, Floating Shock Fitting Via Lagrangian Adaptive Meshes, Technical Paper 95-1721, AIAA Press, Washington, DC, 1995.
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