Incompressible Fluid Flow

Establish the mathematical model of the problem being studied. In Particular, we will introduce the concept of the constitutive equation for a fluid, that is, the relation linking the stress tensor and the velocity gradients. The initial conditions for dynamic cases and the boundary conditions will also be discussed. Discuss the discretization methods for the numerical treatment of the mathematical model. Concentrating on the “velocity-pressure” formulation which is the most appropriate for the general treatment of three dimensional problems, we will present the finite difference and finite element discretization methods. As the advection terms are often dominant in these equations, we will be particularly interested in the upwind schemes. Propose a few applications as examples in order to illustrate the implementation of the proposed methods.