Numerical Simulation and Analysis of Incompressible Newtonian Fluid Flows using FreeFem++

K. R. Mahmud; M. M. Rhaman; A. K. Al Azad

Authors

K. R. Mahmud Department of Computer Science and Engineering, Faculty of School of Science and Engineering, University of Liberal Arts Bangladesh, Dhaka-1209, Bangladesh
M. M. Rhaman Department of Mathematics, Faculty of Science & Information Technology, American International University-Bangladesh, Dhaka-1213, Bangladesh
A. K. Al Azad Department of Computer Science and Engineering, Faculty of School of Science and Engineering, University of Liberal Arts Bangladesh, Dhaka-1209, Bangladesh

Keywords:

Navier-Stokes equations , Newtonian fluids , incompressible flows , pulsatile flow , finite element method , FreeFem

Abstract

We present the analysis and numerical simulations of incompressible Newtonian fluids for unsteady flows in a straight pipe and in deformed pipe with concave and convex deformation of the upper wall. An approach of modeling of blood flow is considered with an unsteady Navier-Stokes problem with a pulsatile flow for which we can establish analogy with existing cardio vascular systems. We apply the Finite Element Methods to obtain solutions and analyze the evolution of the flow over time. For the numerical simulations of fluid flows in complex geometries, FreeFem++ based on finite element method is used and we analyze the behavior of velocity and pressure qualitatively along time.