Flow Computation based on Kinematics

Flows can be classified according to the vorticity distribution as irrotational flows if the vorticity vanishes throughout the domain of flow, vortex flows domi- nated by the presence of compact regions of concentrated vorticity embedded in an otherwise irrotational fluid, and rotational flows if the vorticity is significant throughout the domain of flow. In this chapter, we discuss the kinematic struc- ture and mathematical description of the simplest class of irrotational flows. Following the mathematical analysis, we develop finite-difference methods for computing the velocity field from knowledge of the velocity distribution at the boundaries, and then derive a class of elementary irrotational flows that serve as fundamental building blocks for generating desired solutions. Complemen- tary building blocks associated with elementary vortex flows will provide us with additional elementary units that allow us to address a broader class of irrotational flows where the fluid exhibits circulatory motion.