CRITICAL FLOW AND SPURIOUS SOLUTIONS .2. THE CASE OF N-EQUATIONS

This paper constitutes a continuation of a paper which dealt with the occurrence of spurious solutions in adiabatic two-phase flows through channels of variable cross-sectional area. These are likely to occur i n critical, choked conditions. The problem was straightforward when th e mathematical model consisted of a single, ordinary, nonlinear differ ential equation-which is rare and valid only when the fluid is a perfe ct gas with constant specific heats. In such cases the solution was so ught in the form of an initial-value problem. In the more general, rea listic case the canonical form consists of n greater than or equal to 2 coupled nonlinear equations. This introduces considerable complexity , though the basic topological pattern of the portrait of solutions re mains unchanged. Now it becomes necessary to replace the initial-value problem by one with given boundary conditions. Since critical flows a lways occur in the presence of a singular point in phase space (a sadd le point in the case considered), the boundary there becomes movable. In all cases, spurious solutions are avoided by starting the numerical code at the critical point with analytically determined slopes. Howev er, when n greater than or equal to 2 it becomes necessary to apply an iterative process (''shooting'' method) whose details are described.