Introduction to Computational Fluid Dynamics

6

Equations of Mixed Elliptic–Hyperbolic Type

Model linear equations of parabolic, hyperbolic and elliptic type have been studied respectively in Chapters 3, 4 and 5. The present chapter is devoted to model equations of mixed elliptic–hyperbolic type. Tricomi equation is the model second-order linear partial differential equation of mixed elliptic–hyperbolic type. Formulation of well-posed boundary-value problems for the Tricomi equation has been discussed. A closely related equation of much practical importance is the transonic small perturbation (TSP) equation, which is an approximate equation, governing the steady inviscid transonic flow past a thin profile. It is elliptic in the subsonic part of the flow field, hyperbolic in the supersonic ...