Using the Method of Inverse Problems in Implementing the Solid Immersed Boundaries on Vorticity-Streamfunction Formulation of the Incompressible Viscous Fluid Flow

Sabetghadam, Fereidoun; Shajari-Ghasemkheily, Abdullah

Using the Method of Inverse Problems in Implementing the Solid Immersed Boundaries on Vorticity-Streamfunction Formulation of the Incompressible Viscous Fluid Flow

Authors

Fereidoun Sabetghadam ¹

Abdullah Shajari-Ghasemkheily ²

¹ Aerospace Eng. Dept., Mech. and Aerospace Eng. Faculty, Science and Research Branch, Islamic Azad University, Tehran, Iran.

² Mech. and aerospace Eng. Faculty, Science and research Branch Islamic azad University, Tehran, Iran.

Abstract

A new method is proposed for implementing the no-slip/no-penetration conditions on the irregular immersed boundaries in the vorticity-streamfunction formulation of the incompressible viscous fluid flow. Time integration is performed using a semi-implicit method such that in each time step the vorticity-streamfunction equations are changed to a Helmholtz and a Poisson’s equation. Some singular source terms are added to the right hand sides of these equations, in the solid region, such that the desired boundary conditions can be satisfied. The singular source terms are found, using the inverse problems method, such that the desired boundary conditions of the vorticity-streamfunction equations be satisfied. Since the fast Poisson’s solvers are used, the method is high performance, with the computational effort of O(NlogN); and it is also flexible because it can be applied easily to the complex geometries. The method is applied in simulation of the fluid flow around a square solid obstacle, placed in a channel, and the agreement of the results with the other benchmark results are shown.

Keywords

Incompressible fluid flow

Vorticity-Stream function formulation

Immersed Rigid Body

Singular Source Terms