Computational Fluid Dynamics and Aeroacoustics for Low Mach Number Flow

The main difficulty in the calculation of sound generated by fluid flow at low Mach numbers is the occurrence of quite different scales. While the fluid flow may be affected by small fluid structures containing large energy, such as small vortices in a turbulent flow, the acoustic waves are phenomena of low energy with long wavelengths that may travel over long distances. These different scales and different physical behaviors of fluid flow and sound propagation lead to a difficult task to construct numerical methods for their approximation. The difficulties associated with low Mach number flow are surveyed,e.g. in the paper of Crighton [8].

[1]  Parviz Moin,et al.  Direct computation of the sound from a compressible co-rotating vortex pair , 1992, Journal of Fluid Mechanics.

[2]  H. Guillard,et al.  On the behaviour of upwind schemes in the low Mach number limit , 1999 .

[3]  B. V. Leer,et al.  Towards the Ultimate Conservative Difference Scheme , 1997 .

[4]  R. Sani,et al.  On pressure boundary conditions for the incompressible Navier‐Stokes equations , 1987 .

[5]  Claus-Dieter Munz,et al.  A low Mach number scheme based on multi-scale asymptotics , 2000 .

[6]  J. Bell,et al.  A Second-Order Projection Method for Variable- Density Flows* , 1992 .

[7]  P. Colella,et al.  A second-order projection method for the incompressible navier-stokes equations , 1989 .

[8]  S. Patankar.  Numerical Heat Transfer and Fluid Flow , 2018, Lecture Notes in Mechanical Engineering.

[9]  H. S. Ribner,et al.  The Generation of Sound by Turbulent Jets , 1964 .

[10]  S. Crow,et al.  Aerodynamic Sound Emission as a Singular Perturbation Problem , 1970 .

[11]  James A. Sethian,et al.  THE DERIVATION AND NUMERICAL SOLUTION OF THE EQUATIONS FOR ZERO MACH NUMBER COMBUSTION , 1985 .

[12]  P. Colella,et al.  A Projection Method for Low Speed Flows , 1999 .

[13]  Hester Bijl,et al.  A Unified Method for Computing Incompressible and Compressible Flows in Boundary-Fitted Coordinates , 1998 .

[14]  Cécile Viozat,et al.  Implicit Upwind Schemes for Low Mach Number Compressible Flows , 1997 .

[15]  T. Taylor,et al.  Computational methods for fluid flow , 1982 .

[16]  M. van Dyke.  Perturbation methods in fluid mechanics /Annotated edition/ , 1975 .

[17]  S. Lele.  Compact finite difference schemes with spectral-like resolution , 1992 .

[18]  J. Gillis,et al.  Asymptotic Methods in the Theory of Non‐Linear Oscillations , 1963 .

[19]  Wayne A. Smith,et al.  Preconditioning Applied to Variable and Constant Density Flows , 1995 .

[20]  J. Morrison,et al.  Comparison of the Modified Method of Averaging and the Two Variable Expansion Procedure , 1966 .

[21]  A. Chorin.  Numerical solution of the Navier-Stokes equations , 1968 .

[22]  Andreas Meister,et al.  Asymptotic Single and Multiple Scale Expansions in the Low Mach Number Limit , 1999, SIAM J. Appl. Math..

[23]  D. L. Hawkings,et al.  Sound generation by turbulence and surfaces in arbitrary motion , 1969, Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences.

[24]  M. Lighthill.  On sound generated aerodynamically II. Turbulence as a source of sound , 1954, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[25]  C. Munz,et al.  The extension of incompressible flow solvers to the weakly compressible regime , 2003 .

[26]  A. T. Fedorchenko,et al.  ON SOME FUNDAMENTAL FLAWS IN PRESENT AEROACOUSTIC THEORY , 2000 .

[27]  J. Hardin,et al.  An acoustic/viscous splitting technique for computational aeroacoustics , 1994 .

[28]  D. Spalding,et al.  A calculation procedure for heat, mass and momentum transfer in three-dimensional parabolic flows , 1972 .

[29]  A. Majda,et al.  Compressible and incompressible fluids , 1982 .

[30]  A. Chorin.  A Numerical Method for Solving Incompressible Viscous Flow Problems , 1997 .

[31]  L. Ting,et al.  On vortical flow and sound generation , 1990 .

[32]  C. Rhie.  Pressure-based Navier-Stokes solver using the multigrid method , 1986 .

[33]  C. Tam,et al.  Dispersion-relation-preserving finite difference schemes for computational acoustics , 1993 .

[34]  Marios C. Soteriou,et al.  Development of Computational Aeroacoustics Equations for Subsonic Flows Using a Mach Number Expansion Approach , 2000 .

[35]  B. V. Leer,et al.  Towards the ultimate conservative difference scheme V. A second-order sequel to Godunov's method , 1979 .

[36]  M. Perić,et al.  A collocated finite volume method for predicting flows at all speeds , 1993 .

[37]  J. Kan.  A second-order accurate pressure correction scheme for viscous incompressible flow , 1986 .

[38]  Wei Shyy,et al.  Elements of Pressure-Based Computational Algorithms for Complex Fluid Flow and Heat Transfer , 1994 .

[39]  David L. Darmofal,et al.  Local Preconditioning: Manipulating Mother Nature to Fool Father Time , 1998 .

[40]  Gianfranco Guidati,et al.  Wind Turbine Noise , 1996 .

[41]  R. Klein.  Semi-implicit extension of a Godunov-type scheme based on low Mach number asymptotics , 1995 .

[42]  S. Patankar,et al.  Pressure based calculation procedure for viscous flows at all speeds in arbitrary configurations , 1988 .

[43]  A. Powell.  Theory of Vortex Sound , 1964 .

[44]  M. Lighthill.  On sound generated aerodynamically I. General theory , 1952, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[45]  D. G. Crighton,et al.  Computational Aeroacoustics for Low Mach Number Flows , 1993 .