Contributions to Von Karman Institute lecture series on Computational Fluid dynamics: Advection-diffusion and Navier-Stokes equations

An appropriate starting point for the numerical simulation of fluid flow is the study of the simpler, yet important equation of advection-diffusion (AD), in which the velocity field is presumed to be known. Many fluid flow simulations are primarily concerned with the transport and diffusion of scalar quantitites such as heat (temperature) or concentration (e.g., air pollution). Unfortunately, even in these cases, the more difficult to obtain velocity field must (usually) be computed first. We assume that the velocity is known; later we return to the problem of computing the velocity field itself. Two papers are also included on the finite method for solving the time-dependent, incompressible Navier-Stokes equations.