Publication

Reduced Models for Cardiovascular Applications

2012
Student Projects

Abstract

The goals of this project are to study and numerically solve a reduced fluid-structure interaction problem for cardiovascular applications. The first section of this project presents two test cases in order to understand the finite element method for two dimensional space problems. Then, we focus our attention on the study of the Navier-Stokes equations in a fixed domain. The last section is dedicated to the structure model and the coupling conditions. To avoid the use of the ALE framework and all the numerical issues related to, we use the transpiration conditions of order zero. Finally we point out that thanks to the simplifications the structure equation is embedded in the fluid equations as a generalized Robin boundary condition. The original problem is then reduced to a fluid problem in a moving domain.

Official source

https://infoscience.epfl.ch/entities/publication/fffd3354-c3e8-422e-b1f7-31eaf3b3c1d9

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2012
Student Projects

Abstract

Official source

https://infoscience.epfl.ch/entities/publication/fffd3354-c3e8-422e-b1f7-31eaf3b3c1d9

About this result

Related concepts (32)

Fluid mechanics

Fluid mechanics is the branch of physics concerned with the mechanics of fluids (liquids, gases, and plasmas) and the forces on them. It has applications in a wide range of disciplines, including mechanical, aerospace, civil, chemical, and biomedical engineering, as well as geophysics, oceanography, meteorology, astrophysics, and biology. It can be divided into fluid statics, the study of fluids at rest; and fluid dynamics, the study of the effect of forces on fluid motion.

Navier–Stokes equations

The Navier–Stokes equations (nævˈjeː_stəʊks ) are partial differential equations which describe the motion of viscous fluid substances, named after French engineer and physicist Claude-Louis Navier and Irish physicist and mathematician George Gabriel Stokes. They were developed over several decades of progressively building the theories, from 1822 (Navier) to 1842-1850 (Stokes). The Navier–Stokes equations mathematically express momentum balance and conservation of mass for Newtonian fluids.

Fluid dynamics

In physics, physical chemistry and engineering, fluid dynamics is a subdiscipline of fluid mechanics that describes the flow of fluids—liquids and gases. It has several subdisciplines, including aerodynamics (the study of air and other gases in motion) and hydrodynamics (the study of liquids in motion). Fluid dynamics has a wide range of applications, including calculating forces and moments on aircraft, determining the mass flow rate of petroleum through pipelines, predicting weather patterns, understanding nebulae in interstellar space and modelling fission weapon detonation.