Multiple Solutions and Bifurcation of Finite Difference Approximations to Some Steady Problems of Fluid Dynamics

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.