A least squares formulation of one-dimensional turbulence models

A possible algorithm for resolving coupled Navier-Stokes partial differential equations (PDEs) in turbulent flow is proposed which takes into account the nonlinear terms suggested by turbulence modeling. In order to eliminate temporarily the nonlinear mean convection terms in the PDEs, the technique is applied to the study of fully developed flow between two parallel planes. The possibilities of the algorithm are analyzed successively. The ability of the algorithm to solve PDEs is analyzed, first using models requiring only the mean velocity field and then in the treatment of models involving PDEs for all components of the turbulent stress vector.