A new paradigm for solving Navier-Stokes equations: streamfunction-velocity formulation

We describe the new formulation of the Navier-Stokes equations and use this formulation to solve a couple of fluid flow problems. We use a biconjugate gradient method to obtain the numerical solutions of the fluid flow problems and provide detailed comparison data for the lid driven cavity flow problem. It is discovered that our new formulation successfully provides high accuracy solutions for the benchmark problem. In addition, we also solve a problem of flow in a rectangular cavity with aspect ratio 2 and compare our results qualitatively and quantitatively with numerical and experimental results available in the literature. In all cases, we obtain high accuracy solutions with little additional cost.