×

An efficient multigrid algorithm for compressible reactive flows. (English) Zbl 0935.76053

Summary: This paper presents a parallel multigrid method for computing inviscid and viscous high-speed steady-state reactive flows. The governing equations for reactive flow are solved using an explicit multigrid algorithm, while treating the chemical source terms in a point implicit manner. The convective upwind and split pressure scheme is used to provide necessary artificial dissipation without contaminating the solution. This explicit method yields excellent parallel speedups, thus enabling the calculation of reactive flows with detailed chemical kinetics including large numbers of species and reactions. Results indicate good multigrid speedups and adequate resolution of the reaction zone in both inviscid axisymmetric and viscous two-dimensional hydrogen/oxygen and hydrogen/air test cases. \(\copyright\) Academic Press.

MSC:

76M12 Finite volume methods applied to problems in fluid mechanics
76V05 Reaction effects in flows
76N15 Gas dynamics (general theory)
65Y05 Parallel numerical computation

Software:

CHEMKIN; TRANSPORT
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Belov, A. A., A New Implicit Multigrid-Driven Algorithm for Unsteady Incompressible Flow Calculations on Parallel Computers (1997)
[2] Bussing, T. R.A.; Murman, E. M., Numerical investigation of two-dimensional \(H_2\), J. Propulsion, 3, 448 (1987)
[3] Bussing, T. R.A.; Murman, E. M., Finite-volume method for the calculation of compressible chemically reacting flows, AIAA J., 26, 1070 (1988) · Zbl 0661.76117
[4] Chitsomboon, T.; Kumar, A.; Tiwari, S. N., Numerical Study of Finite-Rate Supersonic Combustion Using Parabolized Equations (1987)
[5] Denton, J. D., An improved time marching method for turbomachinery flow calculations, J. Eng. Gas Turbines Power, 105 (1983) · Zbl 0562.76014
[6] Eberhardt, S.; Imlay, S., Diagonal implicit scheme for computing flows with finite rate chemistry, J. Thermophysics Heat Transfer, 6, 208 (1992)
[7] Eklund, D. R.; Drummond, J. P.; Hassan, H. A., Efficient calculation of chemically reacting flow, AIAA J., 25, 855 (1987)
[8] Eklund, D. R.; Drummond, J. P.; Hassan, H. A., Calculation of supersonic turbulent reacting coaxial jets, AIAA J., 28, 1633 (1990)
[9] Evans, J. S.; Schexnayder, C. J., Influence of chemical kinetics and unmixedness on burning in supersonic hydrogen flames, AIAA J., 18, 180 (1980)
[10] Fielding, J., An Experimental Study of Supersonic Laminar Reacting Boundary Layers (1997)
[11] Gardiner, W. C., Combustion Chemistry (1984)
[12] Gear, C. W., Numerical Initial Value Problems in Ordinary Differential Equations (1971) · Zbl 0217.21701
[13] Jachimowski, C. J., An Analytical Study of the Hydrogen-Air Reactions Mechanism with Application to Scramjet Combustion (1988)
[14] Jameson, A., Solution of the Euler equations for two dimensional transonic flow by a multigrid method, Appl. Math. Comp., 13, 327 (1983) · Zbl 0545.76065
[15] Jameson, A., Multigrid algorithms for compressible flow calculations, Proceedings of the 2nd European Conference on Multigrid Methods, Cologne, 1985, 1228, 166 (1986)
[16] Jameson, A., Analysis and design of numerical schemes for gas dynamics. 1. Artificial diffusion, upwind biasing, limiters and their effect on multigrid convergence, Int. J. Comp. Fluid Dyn., 4, 171 (1995)
[17] Jameson, A., Analysis and design of numerical schemes for gas dynamics. 2. Artificial diffusion and discrete shock structure, Int. J. Comp. Fluid Dyn., 5, 1 (1995)
[18] Ju, Y., Lower-upper scheme for chemically reacting flow with finite rate chemistry, AIAA J., 33, 1418 (1995) · Zbl 0845.76058
[19] Kee, R. J.; Dixon-Lewis, G.; Warnatz, J.; Coltrin, M. E.; Miller, J. A., A Fortran Computer Code Package for the Evaluation of Gas-Phase Multicomponent Transport Properties (1993)
[20] T. J. Kim, R. A. Yetter, F. L. Dryer, New results on moist CO oxidation: High pressure, high temperature experiments and comprehensive kinetic modeling, Twenty-Fifth Symposium (International) on Combustion, The Combustion Institute, 1994; T. J. Kim, R. A. Yetter, F. L. Dryer, New results on moist CO oxidation: High pressure, high temperature experiments and comprehensive kinetic modeling, Twenty-Fifth Symposium (International) on Combustion, The Combustion Institute, 1994
[21] Lehr, H. F., Experiments on shock-induced combustion, Astronautica Acta, 17, 589 (1972)
[22] Liou, M.-S.; Steffen, C. J., A new flux splitting scheme, J. Comput. Phys., 107, 23 (1993) · Zbl 0779.76056
[23] Martinelli, L., Calculation of Viscous Flows with a Multigrid Method (1987)
[24] Martinelli, L.; Jameson, A., Validation of a Multigrid Method for the Reynolds Averaged Equations (1988)
[25] Matsuo, A.; Fujiwara, T., Numerical investigation of oscillatory instability in shock-induced combustion around a blunt body, AIAA J., 31, 1835 (1993)
[26] Matuso, A.; Fujii, K.; Fujiwara, T., Flow features of shock-induced combustion around projectile traveling at hypervelocities, AIAA J., 33, 1056 (1995)
[27] Oran, E. S.; Boris, J. P., Numerical Simulation of Reactive Flow (1987) · Zbl 0762.76098
[28] Palmer, G.; Venkatapathy, E., Comparison of nonequilibrium solution algorithms applied to chemically stiff hypersonic flows, AIAA J., 33, 1211 (1995) · Zbl 0844.76067
[29] Sheffer, S. G., Parallel Computation of Supersonic Reactive Flows with Detailed Chemistry Including Viscous and Species Diffusion Effects (1997)
[30] Sheffer, S. G.; Jameson, A.; Martinelli, L., A Multigrid Method for High Speed Reactive Flows (1997)
[31] Sheffer, S. G.; Jameson, A.; Martinelli, L., Parallel Computation of Supersonic Reactive Flows with Detailed Chemistry (1997)
[32] Shuen, J. S.; Yoon, S., Numerical study of chemically reacting flows using a lower-upper symmetric successive overrelaxation scheme, AIAA J., 27, 1752 (1989)
[33] Sussman, M. A., Source Term Evaluation for Combustion Modeling (1993)
[34] Tatsumi, S.; Martinelli, L.; Jameson, A., Design, Implementation, and Validation of Flux Limited Schemes for the Solution of the Compressible Navier-Stokes Equations (1994)
[35] Tatsumi, S.; Martinelli, L.; Jameson, A., A New High Resolution Scheme for Compressible Viscous Flow with Shocks (1995) · Zbl 0824.76058
[36] Westbrook, C. K., Hydrogen oxidation kinetics in gaseous detonations, Combustion Sci. Tech., 29, 67 (1982)
[37] Williams, F. A., Combustion Theory (1985)
[38] Wilson, G. J.; MacCormack, R. W., Modeling supersonic combustion using a fully implicit numerical method, AIAA J., 30, 1008 (1992)
[39] Wilson, G. J.; Sussman, M. A., Computation of unsteady shock-induced combustion using logarithmic species conservation equations, AIAA J., 31, 294 (1993)
[40] Yee, H. C.; Shinn, J. L., Semi-implicit and fully implicit shock-capturing methods for nonequilibrium flows, AIAA J., 27, 299 (1989)
[41] R. Yetter, J. Fielding, Princeton University, 1996; R. Yetter, J. Fielding, Princeton University, 1996
[42] Yetter, R. A.; Dryer, F. L.; Golden, D. M., Pressure effects on the kinetics of high speed chemically reacting flows, Major Research Topics in Combustion (1992)
[43] Yungster, S., Numerical study of shock-wave/boundary-layer interactions in premixed combustible gases, AIAA J., 30, 2379 (1992) · Zbl 0775.76125
[44] Yungster, S.; Bruckner, A. P., Computational studies of a superdetonative ram accelerator mode, J. Propulsion Power, 8, 457 (1992)
[45] Yungster, S.; Eberhardt, S.; Bruckner, A. P., Numerical simulation of hypervelocity projectiles in detonable gases, AIAA J., 29, 187 (1991)
[46] Yungster, S.; Rabinowitz, M. J., Computation of shock-induced combustion using a detailed methane-air mechanism, J. Propulsion Power, 10, 609 (1994)
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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.