Classification of Fluid Flow Problems and Boundary Conditions

This chapter presents a systematic classification of fluid flow problems based on the type of governing partial differential equations (PDEs) i.e. elliptic, parabolic, and hyperbolic, and their implications in fluid dynamics. The Navier–Stokes equations are highlighted for exhibiting both hyperbolic and parabolic behavior. The chapter also distinguishes between equilibrium problems and marching problems, introducing canonical model equations like the advection, diffusion, and Burgers equations to illustrate key concepts. Practical guidance is offered on choosing appropriate numerical schemes and boundary conditions, with an emphasis on the physical interpretation of mathematical classifications. A short discussion on boundary conditions relevant to CFD applications is included, along with example problems to reinforce conceptual understanding.