Multiple Solutions and Bifurcation of Finite Difference Approximations
to Some Steady Problems of Fluid Dynamics
A.B. Stephens and G.R. Shubin
We review and extend an earlier study of the behavior of multiple
finite difference solutions for a centered difference approximation of the
steady Burgers' equation. Using the fact that all of the inviscid
(viscosity = 0) solutions can be found, we numerically continue these solutions
with respect to viscosity and thereby uncover turning points and bifurcation
points. In addition, we demonstrate analogous behavior for a model of one-
dimensional duct flow and for a particular discretization of the supersonic
blunt body problem.