Conjugate Gradient Method to Solve Fluid Structure Interaction Problem

Abstract

In this paper, we propose a method to solve coupled problem. Our computational method is mainly based on conjugate gradient algorithm. We use finite difference method for the structure and finite element method for the fluid. Conjugate gradient method gives suitable numerical results according to some papers.

Numerical method for unsteady fluid structure interaction problem

“…In this paper, we have presented a method to solve fluid structure interaction problem an unsteady case. This paper also comes to improve the work developed in the former paper [2]. On the one hand, we use finite diffence method and leap-flog scheme to compute for each time the displacement of the structure and the other hand we compute the velocity and the pressure of the fluid for each time in the deformed domain.…”

“…The one we are interested most in this stydy is the blood flow in the arteries. This work is an extension of the method developed in [2]. In this present work we'll focus on a numeric scheme of coupling between a deformed structure and an imcompressible viscous fluid for the calculation of parameters so as the pressure of the fluid, its velocity as well as the displacement of the structure.…”

Numerical simulation of fluid structure interaction benchmark problem with BFGS method

“…Problems involving fluid structure interaction occurs in a wide vatiety of engineering problems and therefore have attracted the interest of many investigations from different engineering disciplines. As a results, much efforts have gone into the development of general computational methods for fluid structure systems [1,2,3,4,5,8,9]. Amongst the computational methods for fluid structure interaction problems, we cite the fixed point method, the Newton method, the Quasi-Newton method, the fictitious domain method.…”