Relaxation control in the solution of CFD problems

A method for changing the relaxation coefficients in the course of the solution of a CFD problem is presented. The aim of the method is to provide, with as little input from the user as possible, the fastest possible (hopefully) approach to convergence. The method draws on elements borrowed from fuzzy-logic theory, which provides an appropriate framework for establishing and applying systematic rules for changing the values of the variables that control a system as a function of the values of some other system variables. The method is tested on several simple but yet typical CFD cases, including Cartesian and curvilinear coordinates, single and multiphase problems, laminar and turbulent flows, inert- and chemically-reacting fluids, and one- to three-dimensional geometries. For these cases, the method is generally well behaved (e.g., non-oscillatory), and provides faster convergence than the use of constant relaxation coefficients for the whole calculation.