An Immersed Boundary Method Based on Navier-Stokes Equations in Discrete Stream Function Formulation

Abstract

A new variant of Immersed Boundary method is proposed in the framework of discrete stream function approach for the INTRODUCTIONThe Immersed Boundary (IB) method is a numerical technique for solving flow problems with complex geometries [1] [2]. This technique has gained popularity recently in the community of computational fluid dynamics due to the great simplification of mesh-generation.The IB method was first introduced by Peskin [3] to simulate flow interacting with elastic boundaries. This method was later extended to handle rigid boundaries by using the direct forcing technique [4] [5]. In IB methods for incompressible flows, most frequently used Navier-Stokes solvers are based on primitivevariable formulation and projection or SIMPLE-type methods. The stream-function vorticity formulation is seldom used in conjunction with the IB method, the only exception to the best of our knowledge is [6]. However, due to the limitation of the stream function-vorticity formulation itself, it can only be ap-