A Stress Mapping Immersed Boundary Method for Viscous Flows

Karim M. Ali; Mohamed Madboul; Hany M. Hamouda; Amr Guaily

Authors

Karim M. Ali Department of Aerospace Engineering, Faculty of Engineering, Cairo University, 12613 Giza, Egypt
Mohamed Madboul Department of Aerospace Engineering, Faculty of Engineering, Cairo University, 12613 Giza, Egypt
Hany M. Hamouda Department of Mathematics, Deanship of Educational Services, Qassim University, P.O. Box 6595 Buraydah 51452, Saudi Arabia
Amr Guaily Smart Engineering Systems Research Center (SESC), Nile University, 12588, Shaikh Zayed City, Egypt

Keywords:

CFD, finite element, immersed boundary, interface, mapping

Abstract

This work introduces an immersed boundary method for two-dimensional simulation of incompressible Navier-Stokes equations. The method uses flow field mapping on the immersed boundary and performs a contour integration to calculate immersed boundary forces. This takes into account the relative location of the immersed boundary inside the background grid elements by using inverse distance weights, and also considers the curvature of the immersed boundary edges. The governing equations of the fluid mechanics are solved using a Galerkin-Least squares finite element formulation. The model is validated against a stationary and a vertically oscillating circular cylinder in a cross flow. The results of the model show acceptable accuracy when compared to experimental and numerical results.