Abstract: To solve unsteady laminar flow problems,a method of velocity-stress-pressure formulation instead of velocity-vorticitypressure formulation is developed.With Newton's linearized method to linearize convective terms and preconditioned conjugate gradient method to solve equations,unsteady stress formulation of Navier-Stokes equations is solved.Comparison between numerical and experimental results of cavity laminar flow shows that result of stress formulation fits experiment better and has higher accuracy than vorticity formulation.The stress formulation can deal with subgrid stress with least squares finite element method.Comparison with experimental results of cavity turbulent flow reveals feasibility of the method.It lays a firm foundation for large eddy simulation computation.

Key words: least squares finite element method, unsteady velocity-stress-pressure, large eddy simulation, cavity flow