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Conservative high-order finite difference schemes for low-Mach number flows. (English) Zbl 0973.76068
Summary: Three finite difference algorithms are proposed to solve a low-Mach number approximation for Navier-Stokes equations. These algorithms exhibit fourth-order spatial and second-order temporal accuracy. They are dissipation-free, and thus well suited for DNS and LES of turbulent flows. The key ingredient common to each of the methods presented is a Poisson equation with variable coefficient that is solved for the hydrodynamic pressure. This feature ensures that the velocity field is constrained correctly. It is shown that this approach is needed to avoid violation of the conservation of kinetic energy in the inviscid limit which would otherwise arise through the pressure term in the momentum equation. An existing set of finite difference formulae for incompressible flow is generalized to handle arbitrary large density fluctuations with no violation of conservation laws through the nonlinear convective terms. An algorithm which conserves mass, momentum, and kinetic energy fully is obtained when an approximate equation of state is used instead of the exact one. Results from a model problem are used to show both spatial and temporal convergence rates, and several test cases illustrate the performance of the algorithms.

76M20 Finite difference methods applied to problems in fluid mechanics
76G25 General aerodynamics and subsonic flows
Full Text: DOI
[1] Majda, A.; Sethian, J., The derivation and numerical solution of the equations for zero Mach number combustion, Combust. sci. technol., 42, 185, (1985)
[2] Ghoniem, A.F.; Knio, O.M., Twenty-first symposium (international) on combustion, 1313, (1986)
[3] McMurthry, P.; Jou, W.; Riley, J.; Metcalfe, R., Direct numerical simulations of a reacting mixing layer with chemical heat release, Aiaa j., 24, 962, (1986)
[4] Knio, O.M.; Worlikar, A.S.; Najm, H.N., Twenty-sixth symposium (international) on combustion, 203, (1996)
[5] Mahalingam, S.; Cantwell, B.J.; Ferziger, J.H., Full numerical simulations of coflowing, axisymmetric jet diffusion flames, Phys. fluids A, 2, 720, (1990)
[6] Cook, A.; Riley, J., Direct numerical simulation of a turbulent reactive plume on a parallel computer, J. comput. phys., 129, 263, (1996) · Zbl 0890.76049
[7] Rutland, C.; Ferziger, J., Simulations of flame-vortex interactions, Combust. flame, 84, 343, (1991)
[8] Najm, H.N.; Wyckoff, P.S.; Knio, O.M., A semi-implicit numerical scheme for reacting flow, J. comput. phys., 143, 381, (1998) · Zbl 0936.76064
[9] Morinishi, Y.; Lund, T.; Vasilyev, O.; Moin, P., Fully conservative higher order finite difference schemes for incompressible flow, J. comput. phys., 143, 90, (1998) · Zbl 0932.76054
[10] Spalart, P., Internal report, Hybrid rkw3+Crank-Nicolson scheme, (1987)
[11] Bell, J.B.; Marcus, D.L., A second-order projection method for variable-density flows, J. comput. phys., 101, 334, (1992) · Zbl 0759.76045
[12] Lai, M., A projection method for reacting flow in the zero Mach number limit, (1993)
[13] Lai, M.; Bell, J.; Colella, P., A projection method for combustion in the zero Mach number limit, (1993)
[14] Concus, P.; Golub, G.H., Use of fast direct methods for the efficient numerical solution of nonseparable elliptic equations, SIAM J. numer. anal., 10, 1103, (1973) · Zbl 0245.65043
[15] Perot, J.B., An analysis of the fractional step method, J. comput. phys., 108, 51, (1993) · Zbl 0778.76064
[16] Suslov, S.; Paolucci, S., Stability of mixed-convection flow in a tall vertical channel under no-Boussinesq conditions, J. fluid mech., 302, 91, (1995) · Zbl 0853.76026
[17] Vasilyev, O.; Paolucci, S., Stability of unstable stratified shear flow in a channel under non-Boussinesq conditions, Acta mech., 112, 37, (1995) · Zbl 0868.76029
[18] Nicoud, F., Numerical study of a channel flow with variable properties, (1998)
[19] F. Nicoud, and, T. Poinsot, Dns of a channel flow with variable properties, in, First International Symposium on Turbulence and Shear Flow Phenomena, Double Tree Resort, Santa Barbara, September 12-15, 1999.
[20] Kim, J.; Moin, P.; Moser, R., Turbulence statistics in fully developed channel flow at low Reynolds number, J. fluid mech., 177, 133, (1987) · Zbl 0616.76071
[21] Kim, J.; Moin, P., Transport of passive scalars in a turbulent channel flow, Turbulent shear flows, 6, 85, (1987)
[22] Van Driest, E.R., Turbulent boundary layer in compressible fluids, J. aeronaut. sci., 18, 145, (1951) · Zbl 0045.12903
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