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A low-dissipation and time-accurate method for compressible multi-component flow with variable specific heat ratios. (English) Zbl 1337.76054
Summary: A low-dissipation method for calculating multi-component gas dynamics flows with variable specific heat ratio that is capable of accurately simulating flows which contain both high- and low-Mach number features is proposed. The technique combines features from the double-flux multi-component model, nonlinear error-controlled WENO, adaptive TVD slope limiters, rotated Riemann solvers, and adaptive mesh refinement to obtain a method that is both robust and accurate. Success of the technique is demonstrated using an extensive series of numerical experiments including premixed deflagrations, Chapman-Jouget detonations, re-shocked Richtmyer-Meshkov instability, shock-wave and hydrogen gas column interaction, and multi-dimensional detonations. This technique is relatively straight-forward to implement using an existing compressible Navier-Stokes solver based on Godunov’s method.

76N15 Gas dynamics (general theory)
76M20 Finite difference methods applied to problems in fluid mechanics
76T99 Multiphase and multicomponent flows
65M50 Mesh generation, refinement, and adaptive methods for the numerical solution of initial value and initial-boundary value problems involving PDEs
Full Text: DOI
[1] K. Kim, W. Wilson, S. Peiris, C. Needham, C. Watry, D. Ortley, F. Zhang, Effects of particle damage during detonation of thermobarics on subsequent reactions, in: 21st International Colloquium on the Dynamics of Explosives and Reactive Systems (ICDERS 21), Poitiers, France, 2007.
[2] Abgrall, R., How to prevent pressure oscillations in multicomponent flow calculations: a quasi conservative approach, Journal of computational physics, 125, 85, 150-160, (1996) · Zbl 0847.76060
[3] Billet, G.; Abgrall, R., An adaptive shock-capturing algorithm for solving unsteady reactive flows, Computers and fluids, 32, 10, 1473-1495, (2003) · Zbl 1033.76031
[4] Kawai, S.; Terashima, H., A high-resolution scheme for compressible multicomponent flows with shock waves, International journal for numerical methods in fluids, 66, 10, 1207-1225, (2011) · Zbl 1432.76274
[5] Housman, J.A.; Kiris, C.C.; Hafez, M.M., Time-derivative preconditioning methods for multicomponent flows. part I: Riemann problems, Journal of applied mechanics, 76, 021210, (2009)
[6] Billet, G., Improvement of convective concentration fluxes in a one step reactive flow solver, Journal of computational physics, 204, 1, 319-352, (2005) · Zbl 1143.76474
[7] Billet, G.; Ryan, J., A runge – kutta discontinuous Galerkin approach to solve reactive flows: the hyperbolic operator, Journal of computational physics, 230, 4, 1064-1083, (2011) · Zbl 1297.76189
[8] Abgrall, R.; Karni, S., Computations of compressible multifluids, Journal of computational physics, 169, 2, 594-623, (2001) · Zbl 1033.76029
[9] Jiang, G.-S.; Shu, C.-W., Efficient implementation of weighted ENO schemes, Journal of computational physics, 126, 202-228, (1996) · Zbl 0877.65065
[10] Balsara, D.S.; Shu, C.-W., Monotonicity preserving weighted essentially non-oscillatory schemes with increasingly high order of accuracy, Journal of computational physics, 160, 405-452, (2000) · Zbl 0961.65078
[11] Van Leer, B., Towards the ultimate conservative difference scheme V. A second-order sequel to godunov’s method, Journal of computational physics, 32, 1, 101-136, (1979) · Zbl 1364.65223
[12] Martín, M.P.; Taylor, E.M.; Wu, M.; Weirs, V.G., A bandwidth-optimized WENO scheme for the effective direct numerical simulation of compressible turbulence, Journal of computational physics, 220, 1, 270-289, (2006) · Zbl 1103.76028
[13] Taylor, E.M.; Wu, M.; Martín, M.P., Optimization of nonlinear error for weighted essentially non-oscillatory methods in direct numerical simulations of compressible turbulence, Journal of computational physics, 223, 1, 384-397, (2007) · Zbl 1165.76350
[14] Kang, H.-M.; Kim, K.H.; Lee, D.-H., A new approach of a limiting process for multi-dimensional flows, Journal of computational physics, 229, 7102-7128, (2010) · Zbl 1425.76185
[15] Kim, K.H.; Kim, C., Accurate, efficient and monotonic numerical methods for multi-dimensional compressible flows. part II: multi-dimensional limiting process, Journal of computational physics, 208, 2, 570-615, (2005) · Zbl 1329.76265
[16] Thornber, B.; Drikakis, D.; Williams, R.J.R.; Youngs, D., On entropy generation and dissipation of kinetic energy in high-resolution shock-capturing schemes, Journal of computational physics, 227, 10, 4853-4872, (2008) · Zbl 1142.65073
[17] Thornber, B.; Mosedale, A.; Drikakis, D.; Youngs, D.; Williams, R., An improved reconstruction method for compressible flows with low Mach number features, Journal of computational physics, 227, 10, 4873-4894, (2008) · Zbl 1388.76188
[18] Kolmogorov, A.N., Dissipation of energy in the locally isotropic turbulence, Proceedings: mathematical and physical sciences, 434, 1890, 15-17, (1991) · Zbl 1142.76390
[19] Drikakis, D.; Hahn, M.; Mosedale, A.; Thornber, B., Large eddy simulation using high-resolution and high-order methods, Philosophical transactions of the royal society A: mathematical physical and engineering sciences, 367, 1899, 2985-2997, (2009) · Zbl 1185.76719
[20] Kim, K.H.; Kim, C., Accurate, efficient and monotonic numerical methods for multi-dimensional compressible flows. part I: spatial discretization, Journal of computational physics, 208, 2, 527-569, (2005) · Zbl 1329.76264
[21] MacNeice, P.; Olson, K.; Mobarry, C.; de Fainchtein, R.; Packer, C., PARAMESH: a parallel adaptive mesh refinement community toolkit, Computer physics communications, 126, 3, 330-354, (2000) · Zbl 0953.65088
[22] E. Goos, A. Burcat, B. Rusnic, Ideal gas thermochemical database with updates from active thermochemical tables. <http://www.garfield.chem.elte.hu/Burcat/burcat.html> (11.10).
[23] Suresh, A.; Huynh, H.T., Accurate monotonicity-preserving schemes with runge – kutta time stepping, Journal of computational physics, 136, 1, 83-99, (1997) · Zbl 0886.65099
[24] Thornber, B.; Mosedale, A.; Drikakis, D., On the implicit large eddy simulations of homogeneous decaying turbulence, Journal of computational physics, 226, 2, 1202-1929, (2007) · Zbl 1219.76027
[25] A.L. Scandaliato, M.S. Liou, AUSM-based high-order solution for euler equations, in: 48th AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition, Orlando, Florida, 2010. · Zbl 1373.76189
[26] Liou, M.S., A sequel to AUSM. part II: AUSM^{+}-up for all speeds, Journal of computational physics, 214, 1, 137-170, (2006) · Zbl 1137.76344
[27] Toro, E.F., Riemann solvers and numerical methods for fluid dynamics, (1999), Springer New York, NY · Zbl 0923.76004
[28] K. Kitamura, E. Shima, Improvement of simple low-dissipation AUSM against shock instabilities in consideration of interfacial speed of sound, in: J. Periera, A. Sequeira (Eds.), V European Conference on Computational Fluid Dynamics ECCOMAS CFD 2010, Lisbon, Portugal, 2010.
[29] Pandolfi, M.; D’Ambrosio, D., Numerical instabilities in upwind methods: analysis and cures for the “carbuncle” phenomenon, Journal of computational physics, 166, 2, 271-301, (2001) · Zbl 0990.76051
[30] Huang, K.; Wu, H.; Yu, H.; Yan, D., Cures for numerical shock instability in HLLC solver, International journal for numerical methods in fluids, 65, 1026-1038, (2011) · Zbl 1428.76120
[31] Spiteri, R.J.; Ruuth, S.J., A new class of optimal high-order strong-stability-preserving time discretization methods, SIAM journal on numerical analysis, 40, 2, 469-491, (2003) · Zbl 1020.65064
[32] Coffee, T.P.; Heimerl, J.M., Transport algorithms for premixed, laminar steady-state flames, Combustion and flame, 43, 273-289, (1981)
[33] Kee, R.J.; Coltrin, M.E.; Glarborg, P., Chemically reacting flow theory and practice, (2003), John Wiley & Sons Hoboken, NJ
[34] R.A. Svehla, Estimated viscosities and thermal conductivities of gases at high temperatures, Technical Report R-132, NASA, 1962.
[35] Ern, A.; Giovangigli, V., Multicomponent transport algorithms, (1994), Springer-Verlag Heidelberg · Zbl 0820.76002
[36] Verwer, J.G.; Sommeijer, B.P.; Hundsdorfer, W., RKC time-stepping for advection – diffusion – reaction problems, Journal of computational physics, 201, 1, 61-79, (2004) · Zbl 1059.65085
[37] G.D. Byrne, S. Thompson, Vode_f90 support page. <http://www.radford.edu/thompson/vodef90web/> (12.10).
[38] Brown, P.N.; Byrne, G.D.; Hindmarsh, A.C., Vode: a variable-coefficient ODE solver, SIAM journal on scientific and statistical computing, 10, 5, 1038-1051, (1989) · Zbl 0677.65075
[39] Berger, M.J.; Oliger, J., Adaptive mesh refinement for hyperbolic partial differential equations, Journal of computational physics, 53, 3, 484-512, (1984) · Zbl 0536.65071
[40] Berger, M.J.; Colella, P., Local adaptive mesh refinement for shock hydrodynamics, Journal of computational physics, 82, 1, 64-84, (1989) · Zbl 0665.76070
[41] Sun, M.; Takayama, K., Conservative smoothing on an adaptive quadrilateral grid, Journal of computational physics, 150, 1, 143-180, (1999) · Zbl 0929.65059
[42] John, J.E.A., Gas dynamics, (1984), Prentice Hall Upper Saddle River, NJ
[43] Poinsot, T.; Veynante, D., Theoretical and numerical combustion, (2001), R.T. Edwards Inc. Philadelphia, PA
[44] Huang, Y.; Risha, G.A.; Yang, V.; Yetter, R.A., Effect of particle size on combustion of aluminum particle dust in air, Combustion and flame, 156, 1, 5-13, (2009)
[45] R.J. Kee, F.M. Rupley, J.A. Miller, M.E. Coltrin, J.F. Grcar, E. Meeks, H.K. Moffat, A.E. Lutz, G. Dixon-Lewis, M.D. Smooke, J. Warnatz, G.H. Evans, R.S. Larson, R.E. Mitchell, L.R. Petzold, W.C. Reynolds, M. Caracotsios, W.E. Stewart, P. Glarborg, C. Wang, C.L. McLellan, O. Adigun, W.G. Houf, C.P. Chou, S.F. Miller, P. Ho, P.D. Young, D.J. Young, D.W. Hodgson, M.V. Petrova, K.V. Puduppakkam, Chemkin 4.1.1, Reaction Design, San Diego, CA, 2007.
[46] Oran, E.S.; Weber, J.W.; Stefaniw, E.I.; Lefebvre, M.H.; Anderson, J.D., A numerical study of a two-dimensional H2-O2-ar detonation using a detailed chemical reaction model, Combustion and flame, 113, 1-2, 147-163, (1998)
[47] R. Deiterding, Parallel adaptive simulation of multi-dimensional detonation structures, Ph.D. Thesis, Branderburg University of Technology Cottbus, 2003.
[48] Westbrook, C.K., Chemical kinetics of hydrocarbon oxidation in gaseous detonations, Combustion and flame, 46, 191-210, (1982)
[49] Nourgaliev, R.R.; Dinh, T.N.; Theofanous, T.G., A pseudocompressibility method for the numerical simulation of incompressible multifluid flows, International journal of multiphase flow, 30, 7-8, 901-937, (2004) · Zbl 1136.76593
[50] Ghia, U.; Ghia, K.N.; Shin, C.T., High-re solutions for incompressible flow using the navier – stokes equations and a multigrid method, Journal of computational physics, 48, 3, 387-411, (1982) · Zbl 0511.76031
[51] Daru, V.; Tenaud, C., Numerical simulation of the viscous shock tube problem by using a high resolution monotonicity-preserving scheme, Computers and fluids, 38, 3, 664-676, (2009) · Zbl 1193.76092
[52] Latini, M.; Schilling, O.; Don, W.S., Effects of weno flux reconstruction order and spatial resolution on reshocked two-dimensional richtmyer – meshkov instability, Journal of computational physics, 221, 2, 805-836, (2007) · Zbl 1107.65338
[53] Billet, G.; Giovangigli, V.; de Gassowski, G., Impact of volume viscosity on a shock-hydrogen-bubble interaction, Combustion theory and modelling, 12, 2, 221-248, (2008) · Zbl 1148.80374
[54] Miller, J.; Mitchell, R.; Smooke, M.; Kee, R., Toward a comprehensive chemical kinetic mechanism for the oxidation of acetylene: comparison of model predictions with results from flame and shock tube experiments, (), 181-196
[55] E. Oran, D. Mott, Chemeq2: A solver for the stiff ordinary differential equations of chemical kinetics, Technical Report NRL/MR/6400-01-8553, Naval Research Laboratory, Washington, DC, 2001.
[56] Lee, J.H., Dynamic parameters of gaseous detonations, Annual review of fluid mechanics, 16, 311-336, (1984)
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