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A Consistent Characteristic Boundary Condition for General Fluid Mixture and Its Implementation in a Preconditioning Scheme

Published online by Cambridge University Press:  03 June 2015

Hua-Guang Li ,
Nan Zong ,
Xi-Yun Lu  and
Vigor Yang
Hua-Guang Li*
Affiliation:
Department of Modern Mechanics, The University of Science and Technology of China, Hefei, Anhui 230026, China School of Aerospace Engineering, The Georgia Institute of Technology, Atlanta, GA 30332, USA
Nan Zong*
Affiliation:
Department of Mechanical and Nuclear Engineering, The Pennsylvania State University, University Park, PA 16802, USA
Xi-Yun Lu*
Affiliation:
Department of Modern Mechanics, The University of Science and Technology of China, Hefei, Anhui 230026, China
Vigor Yang*
Affiliation:
School of Aerospace Engineering, The Georgia Institute of Technology, Atlanta, GA 30332, USA
*
Email: lhg@mail.ustc.edu.cn
Email: zongnan@gmail.com
Email: xlu@ustc.edu.cn
Corresponding author. URL: http://soliton.ae.gatech.edu/people/vigor.yang/. Email: vigor.yang@aerospace.gatech.edu
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Abstract

Characteristic boundary conditions that are capable of handling general fluid mixtures flow at all flow speeds are developed. The formulation is based on fundamental thermodynamics theories incorporated into an efficient preconditioning scheme in a unified manner. Local one-dimensional inviscid (LODI) relations compatible to the preconditioning system are proposed to obtain information carried by incoming characteristic waves at boundaries accurately. The approach has been validated against a variety of sample problems at a broad range of fluid states and flow speeds. Both acoustic waves and hydrodynamic flow features can pass through the boundaries of computational domain transparently without any un-physical reflection or spurious distortion. The approach can be reliably applied to fluid flows at extensive thermodynamic states and flow speeds in numerical simulations. Moreover, the use of the boundary condition shows to improve the computational efficiency.

Keywords

65M1078A48Real-fluidpreconditioning methodmethod of characteristicsLODI relations
Type
Research Article
Information
Advances in Applied Mathematics and Mechanics , Volume 4 , Issue 1 , February 2012 , pp. 72 - 92
Copyright
Copyright © Global-Science Press 2012

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References

[1] Colonius, T., Modeling artificial boundary conditions for compressible flow, Ann. Rev. Fluid. Mech., 36 (2004), pp. 315–345.Google Scholar
[2] Hedstrom, G. W., Nonreflecting boundary conditions for nonlinear hyperbolic systems, J. Comput. Phys., 30 (1979), pp. 222–237.Google Scholar
[3] Thompson, K. W., Time-dependent boundary conditions for hyperbolic systems, J. Comput. Phys., 89 (1987), pp. 439–461.CrossRefGoogle Scholar
[4] Poinsot, T. J. and Lele, S. K., Boundary conditions for direct simulations of compressible viscous flows, J. Comput. Phys., 101 (1992), pp. 104–129.Google Scholar
[5] Baum, M., Poinsot, T. and Thevenin, D., Accurate boundary conditions for multicompo-nent reactive flows, J. Comput. Phys., 116 (1994), pp. 247–261.Google Scholar
[6] Meng, H. and Yang, V., A unified treatment of general fluid thermodynamics and its application to a preconditioning scheme, J. Comput. Phys., 189 (2001), pp. 277–304.Google Scholar
[7] Zappoli, B. and Bailly, D., Anomalous heat transport by the piston effect in supercritical fluids under zero gravity, Phys. Rev. A., 41 (1990), pp. 2264–2267.CrossRefGoogle ScholarPubMed
[8] Okong’o, N. and Bellan, J., Consistent boundary conditions for multicomponent real gas mixtures based on characteristic waves, J. Comput. Phys., 176 (2002), pp. 330–344.CrossRefGoogle Scholar
[9] Choi, Y. H. and Merkle, C. L., The application of preconditioning in viscous flows, J. Com-put. Phys., 105 (1993), pp. 207–223.CrossRefGoogle Scholar
[10] Hsieh, S. Y. and Yang, V., A preconditioned flux-differencing scheme for chemically reacting flows at all Mach numbers, Int. J. Comput. Fluid. Dyn., 8 (1997), pp. 31–49.Google Scholar
[11] Zong, N. and Yang, V., An efficient preconditioning scheme for real fluid mixtures using primitive pressure-temperature variables, Int. J. Comput. Fluid. Dyn., 21 (2007), pp. 217–230.CrossRefGoogle Scholar
[12] Buelow, P. E. O., Convergence Enhancement of Euler and Navier-Stokes Algorithms, Ph.D thesis, The Pennsylvania State University, 1995.Google Scholar
[13] Venkateswaran, S. and Merkel, C. L., Dual time stepping and preconditioning for unsteady computations, AIAA Paper, No. 95-0078, 1995.Google Scholar
[14] Oefelein, J. C. and Yang, V., Modeling high-pressure mixing and combustion processes in liquid rocket engines, J. Propul. Power., 14 (1998), pp. 843–857.Google Scholar
[15] Oefelein, J. C., Mixing and combustion of cryogenic oxygen-hydrogen shear-coaxial jet flames at supercritical pressure, Combust. Sci. Tech., 178 (2006), pp. 229–252.Google Scholar
[16] Rudy, D. H. and Strikwerda, J. C., A nonreflecting outflow boundary condition for subsonic Navier-Stokes calculations, J. Comput. Phys., 18 (1980), pp. 55–70.Google Scholar
[17] Shuen, J. S., Chen, K. H. and Choi, Y. H., A coupled implicit method for chemical non-equilibrium viscous flows at all speeds, J. Comput. Phys., 106 (1993), pp. 306–318.Google Scholar
[18] Jameson, A., The evolution of computational methods in aerodynamics, J. Appl. Math., 50 (1983), pp. 1052–1070.Google Scholar
[19] Rai, M. M. and Chakravarthy, S., Conservative high-order accurate finite difference methods for curvilinear grids, AIAA Paper, No. 1993-3380.Google Scholar
[20] Jorgenson, P. and Turkel, E., Central difference TVD schemes for time dependent and steady state problems, J. Comput. Phys., 107 (1993), pp. 297–308.CrossRefGoogle Scholar
[21] Swanson, R. C. and Turkel, E., On central difference and upwind schemes, J. Comput. Phys., 101 (1992), pp. 292–306.CrossRefGoogle Scholar
[22] Soave, G., Equilibrium constants from a modified Redlich-Kwong equation of state, Chem. Eng. Sci., 27 (1972), pp. 1197–1203.Google Scholar
[23] Jacobsen, R. T. and Stewart, R. B., Thermodynamic of nitrogen including and vapor phase from 63K to 2000K with pressure to 10000 bar, J. Phys. Chem. Ref. Data., 2 (1973), pp. 757– 922.CrossRefGoogle Scholar