JOURNAL OF COMPUTATIONAL PHYSICS 106, 306-3 18 ( 1993)
   A Coupled Implicit Method for Chemical Non-equilibrium Flows at All Speeds
  JIAN-SHUN Sverdrup Technology, Inc., NASA Lewis
SHUEN
Research Center, Cleveland, Ohio 44135
   University of Toledo,
KUO-HUEY NASA Lewis
CHEN
Research Center, Cleveland, Ohio 44135
  Sverdrup
Technology,
Inc.,
AND YUNHO CHOI
NASA Lewis Research Center, Cleveland, Ohio 44135
A time-accurate,
chemical nonequilibrium
Mach numbers. This method employs the strong conservation form of
the governing as unknowns. considered.
equations, but uses primitive variables (p,, u, v, h, Vi)
coupled Navier-Stokes
solution
procedure equations
is described
over a wide range of
Received January
13, 1992
Numerical algorithms developed for compressible flows are often ineffective at low Mach numbers. There are two well-recognized reasons [l-5] for this difficulty. First, the system’s eigenvalues become stiff at low flow velocities. In theory, this can be circumvented by using a large CFL number in implicit schemes. In practice, however, a large approximate factorization error in multidimensions intro- duces the optimum CFL number beyond which con- vergence slows down. At low Mach numbers, there are large disparities among CFL numbers based on each eigenvalue and the numbers cannot become the same optimum number simultaneously. Second, the pressure term in the momen- tum equations becomes singular as the Mach number approaches zero, yielding a large roundoff error. This behavior smears the pressure variation field and often produces inaccurate solutions.