Newton iterative method for potential flow problems based on variational principle and finite element type solution

Abstract

In this article, a new method is presented for simulation of incompressible flow field, which is called Newton iteration based on variational finite element method. Meanwhile, underlying theories and general steps in the solution procedure using this method have been described in detail. In order to validate this method, incompressible simulations on the flowfield around a circular cylinder were conducted. The achieved results were then compared with existing analytic solutions and good agreements have been obtained. In addition, the incompressible flow around an aerofoil was also calculated using both the proposed method and the conventional variational finite element method. It was found that the results obtained by the two methods were exactly the same; however, this proposed method can significantly improve the computational efficiency.