Flow Computation based on Kinematics

Abstract

Flows are classified according to the vorticity distribution as irrotational flows wherein the vorticity vanishes throughout the domain of flow, vortex flows characterized by the presence of compact regions of concentrated vorticity in an otherwise irrotational fluid, and rotational flows wherein the vorticity is significant throughout the domain of flow. In this chapter, we discuss the kinematical structure and mathematical description of the simplest class of irrotational flows. Specifically, we develop finite-difference methods for computing the velocity field from knowledge of the velocity distribution over the boundaries, and derive a class of elementary irrotational flows that serve as building blocks for generating desired solutions. Complementary building blocks associated with elementary vortex flows will provide us with additional degrees of freedom and will allow us to address more general configurations pertinent to a broader class of flow conditions.