A comparison of numerical flux formulas for the Euler and Navier-Stokes equationsNumerical flux formulas for the convection terms in the Euler or Navier-Stokes equations are analyzed with regard to their accuracy in representing steady nonlinear and linear waves (shocks and entropy/shear waves, respectively). Numerical results are obtained for a one-dimensional conical Navier-Stokes flow including both a shock and a boundary layer. Analysis and experiments indicate that for an accurate representation of both layers the flux formula must include information about all different waves by which neighboring cells interact, as in Roe's flux-difference splitting. In comparison, Van Leer's flux-vector splitting, which ignores the linear waves, badly diffuses the boundary layer. The results of MacCormack's scheme, if properly tuned, are significantly better. The use of a sufficiently detailed flux formula appears to reduce the number of cells required to resolve a boundary layer by a factor 1/2 to 1/4 and thus pays off.
Document ID
19870054779
Acquisition Source
Legacy CDMS
Document Type
Conference Paper
Authors
Van Leer, Bram (Michigan, University Ann Arbor, United States)
Thomas, James L. (NASA Langley Research Center Hampton, VA, United States)
Roe, Philip L. (Cranfield Institute of Technology United Kingdom)
Newsome, Richard W. (NASA Langley Research Center; USAF, Wright Aeronautical Laboratories, Hampton VA, United States)