A staggered compact finite difference formulation for the compressible Navier-Stokes equations

In this paper, a compact high order (up to 12th order) numerical method to solve the compressible Navier-Stokes equations will be presented. A staggered arrangement of the variables has been used. It is shown that the method is not only very accurate but numerically also very stable even in the case that not all the energy containing scales in the flow are resolved. This in contrast to standard (collocated) compact finite difference methods. Some results for a turbulent non-reacting and a reacting jet with a Reynolds number of 10,000 and a Mach number of 0.5 are reported.

[1]  F. Harlow,et al.  Numerical Calculation of Time‐Dependent Viscous Incompressible Flow of Fluid with Free Surface , 1965 .

[2]  A. Veldman,et al.  Symmetry-preserving discretization of turbulent flow , 2003 .

[3]  J. Lumley,et al.  Turbulence measurements in axisymmetric jets of air and helium. Part 1. Air jet , 1993, Journal of Fluid Mechanics.

[4]  P. Moin,et al.  DIRECT NUMERICAL SIMULATION: A Tool in Turbulence Research , 1998 .

[5]  Geert Brethouwer,et al.  A numerical investigation on the effect of the inflow conditions on the self-similar region of a round jet , 1998 .

[6]  P. Chu,et al.  A Three-Point Combined Compact Difference Scheme , 1998 .

[7]  Tapan K. Sengupta,et al.  Analysis of central and upwind compact schemes , 2003 .

[8]  Joel H. Ferziger,et al.  A robust high-order compact method for large eddy simulation , 2003 .

[9]  B. Boersma,et al.  Simulation of the mixing of a passive scalar in a round turbulent jet , 2001 .

[10]  M. Carpenter,et al.  Several new numerical methods for compressible shear-layer simulations , 1994 .

[11]  H. Pitsch,et al.  Large-eddy simulation of a turbulent piloted methane/air diffusion flame (Sandia flame D) , 2000 .

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

[13]  Krishnan Mahesh,et al.  High order finite difference schemes with good spectral resolution , 1997 .

[14]  J. Freund.  Noise sources in a low-Reynolds-number turbulent jet at Mach 0.9 , 2001, Journal of Fluid Mechanics.

[15]  William K. George,et al.  Velocity measurements in a high-Reynolds-number, momentum-conserving, axisymmetric, turbulent jet , 1994, Journal of Fluid Mechanics.

[16]  Graham Ashcroft,et al.  Optimized prefactored compact schemes , 2003 .