An application of the numerical solution of nonlinear problems in fluid mechanics using least squares and finite element methods, to unsteady Navier-Stokes equations

A calculation method for viscous fluid flow at mid-range Reynolds numbers is presented. Application to the formulation of a computer program for the numerical simulation of separated turbulent flow at large Reynolds numbers, adding to the Navier-Stokes equations either a classic turbulence model or a homogenized random turbulence expression, is shown. The use of optimal control theory with a distributed parameter system to adjust the parameters so as to assure convergence of the algorithm and to permit the use of smaller computers is also proposed. As for the treatment of nonlinearities, gradient conjugates which have been conditioned to be unconditionally stable in time are suggested.