On the Incompressible Limit of Compressible Fluid Flow

  • M. Hafez
Conference paper
Part of the Notes on Numerical Fluid Mechanics (NNFM) book series (NNFM, volume 78)


Some of the standard formulations of compressible fluid flow simulations are not valid when the Mach number approaches zero. Since, there is no physical singularity at zero Mach number, unified formulations for both compressible and incompressible flows can be found using non-dimensionalizetion and dependent variables different from the standard ones. Potential and Boundary layer equations are examined first and the calculations of the pressure and skin friction coefficients are discussed in the limit of zero Mach number for compressible fluids. For Euler and Navier-Stokes equations, two sets of variables describing the fluid motion are considered the first using temperature, pressure and velocities, and the second using velocities, entropy and total enthalpy. The incompressible isothermal flow limit is recovered as Mach number vanishes in both cases. Flows with heat transfer are also examined. The present formulations can be viewed as preconditioning the standard formulations at the differential level.


Mach Number Supersonic Flow Incompressible Flow Compressible Fluid Boundary Layer Equation 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • M. Hafez
    • 1
  1. 1.Department of Mechanical and Aeronautical EngineeringUniversity of CaliforniaDavisUSA

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