Least Square Solution of Non Linear Problems in Fluid Dynamics

Abstract

Publisher Summary This chapter describes the least square solution of nonlinear problems in fluid dynamics. It discusses the way in which some principles can be applied to the numerical solution of two important problems in fluid mechanics—namely, (1) the transonic flow of an isentropic, compressible perfect fluid and (2) Navier–Stokes equations for incompressible fluids. The theoretical and numerical studies of transonic flows for perfect fluids have always been very important, but these problems have become important in relation with the design and development of large subsonic aircrafts. These transonic problems are very difficult, theoretically and numerically, for the following reasons: (1)tThey are nonlinear, (2) shocks may exist in the flow, and (3) an entropy condition is needed, in a way or another, to avoid nonphysical solutions. This chapter describes an approach that seems very convenient for computing flows past profiles, subsonic at infinity, or flows in nozzles. Some indications are also given in the chapter on the minimization of nonquadratic functionals by conjugate gradient algorithms.