Articles de revues : « Low-Mach number flows »

1

Alazard, Thomas. « Low Mach Number Flows and Combustion ». SIAM Journal on Mathematical Analysis 38, n^o 4 (janvier 2006) : 1186–213. http://dx.doi.org/10.1137/050644100.

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Dwyer, Harry A. « Calculation of low Mach number reacting flows ». AIAA Journal 28, n^o 1 (janvier 1990) : 98–105. http://dx.doi.org/10.2514/3.10358.

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3

Pozorski, J., et A. Kajzer. « Density diffusion in low Mach number flows ». Journal of Physics : Conference Series 2367, n^o 1 (1 novembre 2022) : 012027. http://dx.doi.org/10.1088/1742-6596/2367/1/012027.

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Abstract In the realm of compressible viscous flow modelling, we briefly revisit the debate on a possible inconsistency of the Navier-Stokes (NS) equations. Then, we recall a recent proposal from the literature, put forward by M. Svärd. One of its features is the mass diffusive term in the continuity equation. The presence of density diffusion in the Svärd model reduces dispersive numerical errors when simple centred 2nd order, numerical diffusion free, spatial schemes are used, as confirmed in the simulations of a doubly-periodic shear layer at Ma = 0.05 and Re = 104. Further reduction of the dispersive errors at the spatial discretisation level is possible by more sophisticated approximation techniques.

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4

Penel, Yohan, Stephane Dellacherie et Bruno Després. « Coupling strategies for compressible-low Mach number flows ». Mathematical Models and Methods in Applied Sciences 25, n^o 06 (24 mars 2015) : 1045–89. http://dx.doi.org/10.1142/s021820251550027x.

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In order to enrich the modeling of fluid flows, we investigate in this paper a coupling between two models dedicated to distinct regimes. More precisely, we focus on the influence of the Mach number as the low Mach case is known to induce theoretical and numerical issues in a compressible framework. A moving interface is introduced to separate a compressible model (Euler with source term) and its low Mach counterpart through relevant transmission conditions. A global steady state for the coupled problem is exhibited. Numerical simulations are then performed to highlight the influence of the coupling by means of a robust numerical strategy.

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Filippova, O., et D. Hänel. « Lattice-BGK Model for Low Mach Number Combustion ». International Journal of Modern Physics C 09, n^o 08 (décembre 1998) : 1439–45. http://dx.doi.org/10.1142/s0129183198001308.

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For the simulation of low Mach number reactive flows with significant density changes a modified lattice-BGK model in combination with the conventional convective-diffusion solvers for equations of temperature and species is proposed. Together with boundary-fitting conditions and local grid refinement the scheme enables the accurate consideration of low Mach number combustion in complex geometry as the flows around porous burners or droplets combustion.

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Duarte, Max, Ann S. Almgren et John B. Bell. « A Low Mach Number Model for Moist Atmospheric Flows ». Journal of the Atmospheric Sciences 72, n^o 4 (31 mars 2015) : 1605–20. http://dx.doi.org/10.1175/jas-d-14-0248.1.

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Abstract A low Mach number model for moist atmospheric flows is introduced that accurately incorporates reversible moist processes in flows whose features of interest occur on advective rather than acoustic time scales. Total water is used as a prognostic variable, so that water vapor and liquid water are diagnostically recovered as needed from an exact Clausius–Clapeyron formula for moist thermodynamics. Low Mach number models can be computationally more efficient than a fully compressible model, but the low Mach number formulation introduces additional mathematical and computational complexity because of the divergence constraint imposed on the velocity field. Here, latent heat release is accounted for in the source term of the constraint by estimating the rate of phase change based on the time variation of saturated water vapor subject to the thermodynamic equilibrium constraint. The authors numerically assess the validity of the low Mach number approximation for moist atmospheric flows by contrasting the low Mach number solution to reference solutions computed with a fully compressible formulation for a variety of test problems.

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Woosely, S. E., A. J. Aspden, J. B. Bell, A. R. Kerstein et V. Sankaran. « Numerical simulation of low Mach number reacting flows ». Journal of Physics : Conference Series 125 (1 juillet 2008) : 012012. http://dx.doi.org/10.1088/1742-6596/125/1/012012.

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8

Shimomura, Yutaka. « Turbulent transport modeling in low Mach number flows ». Physics of Fluids 11, n^o 10 (octobre 1999) : 3136–49. http://dx.doi.org/10.1063/1.870171.

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9

Bell, J. B., A. J. Aspden, M. S. Day et M. J. Lijewski. « Numerical simulation of low Mach number reacting flows ». Journal of Physics : Conference Series 78 (1 juillet 2007) : 012004. http://dx.doi.org/10.1088/1742-6596/78/1/012004.

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10

Schochet, Steven. « The mathematical theory of low Mach number flows ». ESAIM : Mathematical Modelling and Numerical Analysis 39, n^o 3 (mai 2005) : 441–58. http://dx.doi.org/10.1051/m2an:2005017.

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Danchin, Raphaël. « Low Mach number limit for viscous compressible flows ». ESAIM : Mathematical Modelling and Numerical Analysis 39, n^o 3 (mai 2005) : 459–75. http://dx.doi.org/10.1051/m2an:2005019.

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12

Mary, Ivan, Pierre Sagaut et Michel Deville. « An algorithm for low Mach number unsteady flows ». Computers & ; Fluids 29, n^o 2 (février 2000) : 119–47. http://dx.doi.org/10.1016/s0045-7930(99)00007-9.

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13

Alì, G. « Low Mach Number Flows in Time-Dependent Domains ». SIAM Journal on Applied Mathematics 63, n^o 6 (janvier 2003) : 2020–41. http://dx.doi.org/10.1137/s0036139902400738.

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14

Xu, Jian-Hua, Wen-Ping Song, Zhong-Hua Han et Zi-Hao Zhao. « Effect of mach number on high-subsonic and low-Reynolds-number flows around airfoils ». International Journal of Modern Physics B 34, n^o 14n16 (3 juin 2020) : 2040112. http://dx.doi.org/10.1142/s0217979220401128.

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High-subsonic and low-Reynolds-number flow is a special aerodynamic problem associated with near space propellers and Mars aircrafts. The flow around airfoils and the corresponding aerodynamic performance are different from the incompressible flow at low-Reynolds-number, due to complex shock wave-laminar separation bubble interaction. The objective of this paper is to figure out the effect of Mach number on aerodynamic performance and special flow structure of airfoil. An in-house Reynolds-averaged Navier–Stokes solver coupled with [Formula: see text] transition model is employed to simulate the flows around the E387 airfoil. The results show that the lift slope is larger than [Formula: see text] in the linear region. No stall occurs even at an attack angle of [Formula: see text]. With increase of Mach number, lift coefficient decreases when attack angle is below [Formula: see text]. However, once the angle of attack exceeds [Formula: see text], higher Mach number corresponds to higher lift coefficient. In addition, the strength and number of shock waves are very sensitive to Mach number. With increase of Mach number, the region of reverse flow vortex near transition location becomes smaller and finally disappears, while a new reverse flow vortex appears near the trailing edge and becomes larger.

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15

Feireisl, Eduard, et Hana Petzeltová. « Low Mach number asymptotics for reacting compressible fluid flows ». Discrete & ; Continuous Dynamical Systems - A 26, n^o 2 (2010) : 455–80. http://dx.doi.org/10.3934/dcds.2010.26.455.

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16

Filippova, Olga. « Multiscale lattice Boltzmann schemes for low Mach number flows ». Philosophical Transactions of the Royal Society of London. Series A : Mathematical, Physical and Engineering Sciences 360, n^o 1792 (15 mars 2002) : 467–76. http://dx.doi.org/10.1098/rsta.2001.0954.

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17

Teleaga, Ioan, et Mohammed Seaïd. « Simplified radiative models for low-Mach number reactive flows ». Applied Mathematical Modelling 32, n^o 6 (juin 2008) : 971–91. http://dx.doi.org/10.1016/j.apm.2007.02.021.

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18

Ou, Yaobin. « Low Mach number limit of viscous polytropic fluid flows ». Journal of Differential Equations 251, n^o 8 (octobre 2011) : 2037–65. http://dx.doi.org/10.1016/j.jde.2011.07.009.

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19

Hu, Xianpeng, et Dehua Wang. « Low Mach Number Limit of Viscous Compressible Magnetohydrodynamic Flows ». SIAM Journal on Mathematical Analysis 41, n^o 3 (janvier 2009) : 1272–94. http://dx.doi.org/10.1137/080723983.

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Teleaga, Ioan, Mohammed Seaïd, Ingenuin Gasser, Axel Klar et Jens Struckmeier. « Radiation models for thermal flows at low Mach number ». Journal of Computational Physics 215, n^o 2 (juillet 2006) : 506–25. http://dx.doi.org/10.1016/j.jcp.2005.11.015.

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21

Metzner, M., et G. Wittum. « Computing low Mach number flows by parallel adaptive multigrid ». Computing and Visualization in Science 9, n^o 4 (20 octobre 2006) : 259–69. http://dx.doi.org/10.1007/s00791-006-0025-x.

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22

Shima, Eiji, et Keiichi Kitamura. « New approaches for computation of low Mach number flows ». Computers & ; Fluids 85 (octobre 2013) : 143–52. http://dx.doi.org/10.1016/j.compfluid.2012.11.017.

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23

Lange, H. C. de. « Split time-integration for low Mach number compressible flows ». Communications in Numerical Methods in Engineering 20, n^o 7 (23 avril 2004) : 501–9. http://dx.doi.org/10.1002/cnm.687.

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24

Meister, A. « Asymptotic based preconditioning technique for low Mach number flows ». ZAMM 83, n^o 1 (janvier 2003) : 3–25. http://dx.doi.org/10.1002/zamm.200310002.

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25

Meister, A. « Asymptotic based preconditioning technique for low Mach number flows ». ZAMM 83, n^o 4 (19 avril 2003) : 287–88. http://dx.doi.org/10.1002/zamm.200390008.

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26

Chakravorty, Saugata, et Joseph Mathew. « A high-resolution scheme for low Mach number flows ». International Journal for Numerical Methods in Fluids 46, n^o 3 (17 août 2004) : 245–61. http://dx.doi.org/10.1002/fld.741.

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27

Lee, Sang-Hyeon. « Effects of condition number on preconditioning for low Mach number flows ». Journal of Computational Physics 231, n^o 10 (mai 2012) : 4001–14. http://dx.doi.org/10.1016/j.jcp.2012.02.004.

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28

VARSAKELIS, C., et M. V. PAPALEXANDRIS. « Low-Mach-number asymptotics for two-phase flows of granular materials ». Journal of Fluid Mechanics 669 (12 janvier 2011) : 472–97. http://dx.doi.org/10.1017/s0022112010005173.

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In this paper, we generalize the concept of low-Mach-number approximation to multi-phase flows and apply it to the two-phase flow model of Papalexandris (J. Fluid Mech., vol. 517, 2004, p. 103) for granular materials. In our approach, the governing system of equations is first non-dimensionalized with values that correspond to a reference thermodynamic state of the phase with the smaller speed of sound. By doing so, the Mach number based on this reference state emerges as a perturbation parameter of the equations in hand. Subsequently, we expand each variable in power series of this parameter and apply singular perturbation techniques to derive the low-Mach-number equations. As expected, the resulting equations are considerably simpler than the unperturbed compressible equations. Our methodology is quite general and can be directly applied for the systematic reduction of continuum models for granular materials and for many different types of multi-phase flows. The structure of the low-Mach-number equations for two special cases of particular interest, namely, constant-density flows and the equilibrium limit is also discussed and analysed. The paper concludes with some proposals for experimental validation of the equations.

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29

Both, A., O. Lehmkuhl, D. Mira et M. Ortega. « Low-dissipation finite element strategy for low Mach number reacting flows ». Computers & ; Fluids 200 (mars 2020) : 104436. http://dx.doi.org/10.1016/j.compfluid.2020.104436.

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Fu, Jian-Ming, Hai-Min Tang et Hong-Quan Chen. « Rapid computation of rotary derivatives for subsonic and low transonic flows ». Engineering Computations 36, n^o 9 (11 novembre 2019) : 3108–21. http://dx.doi.org/10.1108/ec-09-2018-0399.

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Purpose The purpose of this paper is to develop a new approach for rapid computation of subsonic and low-transonic rotary derivatives with the available steady solutions obtained by Euler computational fluid dynamics (CFD) codes. Design/methodology/approach The approach is achieved by the perturbation on the steady-state pressure of Euler CFD codes. The resulting perturbation relation is established at a reference Mach number between rotary derivatives and normal velocity on surface due to angular velocity. The solution of the reference Mach number is generated technically by Prandtl–Glauert compressibility correction based on any Mach number of interest under the assumption of simple strip theory. Rotary derivatives of any Mach number of interest are then inversely predicted by the Prandtl–Glauert rule based on the reference Mach number aforementioned. Findings The resulting method has been verified for three typical different cases of the Basic Finner Reference Projectile, the Standard Dynamics Model Aircraft and the Orion Crew Module. In comparison with the original perturbation method, the performance at subsonic and low-transonic Mach numbers has significantly improved with satisfactory accuracy for most design efforts. Originality/value The approach presented is verified to be an efficient way for computation of subsonic and low-transonic rotary derivatives, which are performed almost at the same time as an accounting solution of steady Euler equations.

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HU, ZHIWEI, CHRISTOPHER L. MORFEY et NEIL D. SANDHAM. « Sound radiation in turbulent channel flows ». Journal of Fluid Mechanics 475 (25 janvier 2003) : 269–302. http://dx.doi.org/10.1017/s002211200200277x.

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Lighthill’s acoustic analogy is formulated for turbulent channel flow with pressure as the acoustic variable, and integrated over the channel width to produce a two-dimensional inhomogeneous wave equation. The equivalent sources consist of a dipole distribution related to the sum of the viscous shear stresses on the two walls, together with monopole and quadrupole distributions related to the unsteady turbulent dissipation and Reynolds stresses respectively. Using a rigid-boundary Green function, an expression is found for the power spectrum of the far-field pressure radiated per unit channel area. Direct numerical simulations (DNS) of turbulent plane Poiseuille and Couette flow have been performed in large computational domains in order to obtain good resolution of the low-wavenumber source behaviour. Analysis of the DNS databases for all sound radiation sources shows that their wavenumber–frequency spectra have non-zero limits at low wavenumber. The sound power per unit channel area radiated by the dipole distribution is proportional to Mach number squared, while the monopole and quadrupole contributions are proportional to the fourth power of Mach number. Below a particular Mach number determined by the frequency and radiation direction, the dipole radiation due to the wall shear stress dominates the far field. The quadrupole takes over at Mach numbers above about 0.1, while the monopole is always the smallest term. The resultant acoustic field at any point in the channel consists of a statistically diffuse assembly of plane waves, with spectrum limited by damping to a value that is independent of Mach number in the low-M limit.

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32

Sheng, Chunhua. « A Preconditioned Method for Rotating Flows at Arbitrary Mach Number ». Modelling and Simulation in Engineering 2011 (2011) : 1–17. http://dx.doi.org/10.1155/2011/537464.

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An improved preconditioning is proposed for viscous flow computations in rotating and nonrotating frames at arbitrary Mach numbers. The key to the current method is the use of both free stream Mach number and rotating Mach number to construct a preconditioning matrix, which is applied to the compressible governing equations written in terms of primitive variables. A Fourier analysis is conducted that reveals the efficacy of the modified preconditioning. Numerical approximations for the convective and diffusive fluxes are detailed based on the preconditioned system of equations. A set of boundary conditions using characteristic variables are described for internal and external flow computations. Numerical validations are performed on four realistic viscous flows in both fixed and rotating frames. The results indicated that the modified preconditioning has a superior performance compared to the original method to predict flows from extremely low to supersonic Mach numbers.

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33

Pebay, P. P., H. N. Najm et J. G. Pousin. « A Non Split Projection Strategy for Low Mach Number Flows ». International Journal for Multiscale Computational Engineering 2, n^o 3 (2004) : 445–60. http://dx.doi.org/10.1615/intjmultcompeng.v2.i3.60.

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34

Sabanca, Murat, Gunther Brenner et Franz Durst. « Error Control and Adaptivity for Low-Mach-Number Compressible Flows ». AIAA Journal 40, n^o 11 (novembre 2002) : 2234–40. http://dx.doi.org/10.2514/2.1585.

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35

HASEGAWA, Tatsuya. « Numerical Analysis of Combustion in Low Mach Number Turbulent Flows. » Journal of the Japan Society for Aeronautical and Space Sciences 41, n^o 470 (1993) : 141–47. http://dx.doi.org/10.2322/jjsass1969.41.141.

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Sabanca, M., G. Brenner et E. Durst. « Error control and adaptivity for low-Mach-number compressible flows ». AIAA Journal 40 (janvier 2002) : 2234–40. http://dx.doi.org/10.2514/3.15315.

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37

Bassi, F., C. De Bartolo, R. Hartmann et A. Nigro. « A discontinuous Galerkin method for inviscid low Mach number flows ». Journal of Computational Physics 228, n^o 11 (juin 2009) : 3996–4011. http://dx.doi.org/10.1016/j.jcp.2009.02.021.

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Sabanca, Murat, Gunther Brenner et Nafiz Alemdaro?lu. « Improvements to compressible Euler methods for low-Mach number flows ». International Journal for Numerical Methods in Fluids 34, n^o 2 (2000) : 167–85. http://dx.doi.org/10.1002/1097-0363(20000930)34:2<167 ::aid-fld53>3.0.co;2-r.

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39

Gauthier, Serge, et Nicolas Schneider. « Low- and zero-Mach-number models for Rayleigh–Taylor flows ». Computers & ; Fluids 151 (juin 2017) : 85–90. http://dx.doi.org/10.1016/j.compfluid.2017.02.015.

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40

Zhang, Xiao, Joseph D. Chung, Carolyn R. Kaplan et Elaine S. Oran. « The barely implicit correction algorithm for low-Mach-Number flows ». Computers & ; Fluids 175 (octobre 2018) : 230–45. http://dx.doi.org/10.1016/j.compfluid.2018.08.019.

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41

Fortenbach, Roland, et Claus-Dieter Munz. « Multiscale Considerations for Sound Generation in Low Mach Number Flows ». PAMM 2, n^o 1 (mars 2003) : 396–97. http://dx.doi.org/10.1002/pamm.200310182.

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42

LI, CHIN-HSIEN, et ROLAND GLOWINSKI. « MODELLING AND NUMERICAL SIMULATION OF LOW-MACH-NUMBER COMPRESSIBLE FLOWS ». International Journal for Numerical Methods in Fluids 23, n^o 2 (30 juillet 1996) : 77–103. http://dx.doi.org/10.1002/(sici)1097-0363(19960730)23:2<77 ::aid-fld403>3.0.co;2-1.

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Bell, J. B., M. S. Day, A. S. Almgren, M. J. Lijewski et C. A. Rendleman. « A parallel adaptive projection method for low Mach number flows ». International Journal for Numerical Methods in Fluids 40, n^o 1-2 (2002) : 209–16. http://dx.doi.org/10.1002/fld.310.

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Li, Nan, Feng Qu, Di Sun et Guanghui Wu. « An Effective AUSM-Type Scheme for Both Cases of Low Mach Number and High Mach Number ». Applied Sciences 12, n^o 11 (27 mai 2022) : 5464. http://dx.doi.org/10.3390/app12115464.

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A new scheme called AUSMAS (Advection Upstream Splitting Method for All Speeds) is proposed for both high speed and low speed simulation cases. For the cases of low speed, it controls the checkerboard decoupling by keeping the coefficient of the pressure difference to the order of O(Ma−1) in the mass flux. Furthermore, it is able to guarantee a high level of accuracy by keeping the coefficients of the dissipation terms to the order of O(Ma0) in the momentum flux. For the cases of high speeds, especially at supersonic and hypersonic speeds, it is able to avoid the appearance of the shock anomaly by controlling the coefficients of the density perturbation in the mass flux. AUSMAS is testified to have the following attractive properties according to various numerical tests: (1) robustness against the abnormal shock; (2) high resolution in discontinuity; (3) the appearance of the unphysical expansion shock is avoided; (4) high resolution and low dissipation at low speeds; (5) independent of any tuning coefficient. These properties determined that AUSMAS has great promise in efficiently and accurately simulating flows of all speeds.

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Tyliszczak, Artur. « Projection method for high-order compact schemes for low Mach number flows in enclosures ». International Journal of Numerical Methods for Heat & ; Fluid Flow 24, n^o 5 (27 mai 2014) : 1141–74. http://dx.doi.org/10.1108/hff-07-2012-0167.

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Purpose – Variable density flows play an important role in many technological devices and natural phenomena. The purpose of this paper is to develop a robust and accurate method for low Mach number flows with large density and temperature variations. Design/methodology/approach – Low Mach number approximation approach is used in the paper combined with a predictor-corrector method and accurate compact scheme of fourth and sixth order. A novel algorithm is formulated for the projection method in which the boundary conditions for the pressure are implemented in such a way that the continuity equation is fulfilled everywhere in the computational domain, including the boundary nodes. Findings – It is shown that proposed implementation of the boundary conditions considerably improves a solution accuracy. Assessment of the accuracy was performed based on the constant density Burggraf flow and for two benchmark cases for the natural convection problems: steady flow in a square cavity and unsteady flow in a tall cavity. In all the cases the results agree very well with exemplary solutions. Originality/value – A staggered or half-staggered grid arrangement is usually used for the projection method for both constant and low Mach number flows. The staggered approach ensures stability and strong pressure-velocity coupling. In the paper a high-order compact method has been implemented in the framework of low Mach number approximation on collocated meshes. The resulting algorithm is accurate, robust for large density variations and is almost free from the pressure oscillations.

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Zeifang, Jonas, Klaus Kaiser, Andrea Beck, Jochen Schütz et Claus-Dieter Munz. « Efficient high-order discontinuous Galerkin computations of low Mach number flows ». Communications in Applied Mathematics and Computational Science 13, n^o 2 (25 septembre 2018) : 243–70. http://dx.doi.org/10.2140/camcos.2018.13.243.

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Kolb, Elena, et Michael Schäfer. « Aeroacoustic simulation of flexible structures in low Mach number turbulent flows ». Computers & ; Fluids 227 (septembre 2021) : 105020. http://dx.doi.org/10.1016/j.compfluid.2021.105020.

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Gunzburger, Max D., et O. Yu Imanuvilov. « Optimal control of stationary, low Mach number, highly nonisothermal, viscous flows ». ESAIM : Control, Optimisation and Calculus of Variations 5 (2000) : 477–500. http://dx.doi.org/10.1051/cocv:2000118.

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Pradera-Mallabiabarrena, Ainara, Graeme Keith, Finn Jacobsen, Alejandro Rivas et Nere Gil-Negrete. « Practical Computational Aeroacoustics for Compact Surfaces in Low Mach Number Flows ». Acta Acustica united with Acustica 97, n^o 1 (1 janvier 2011) : 14–23. http://dx.doi.org/10.3813/aaa.918382.

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Klein, Rupert. « Multiple spatial scales in engineering and atmospheric low Mach number flows ». ESAIM : Mathematical Modelling and Numerical Analysis 39, n^o 3 (mai 2005) : 537–59. http://dx.doi.org/10.1051/m2an:2005022.

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