Abstract
The existence of multiple steady states with the same farfield behavior is discussed for simple 1-D transonic model problems. These multiple solutions all have only entropy satisfying compressive steady shock waves. Only some of these solutions are stable in the time-dependent system and are accessible through physical time-dependent perturbations. This is demonstrated by some elementary explicit solutions in a scalar model problem. However, for a large class of initial data and large C.F.L. numbers, numerical experiments show that implicit schemes can converge to the physically unstable steady states and this phenomenon is analysed. The scalar model is also discussed as a very simple numerical test problem for implicit schemes with rich structure in both the steady state and time-dependent regimes.
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