Modeling Elastic Vessels with the LBGK Method in Three Dimensions

Abstract

The Lattice Bhatnagar Gross and Krook (LBGK) method is widely used to solve fluid mechanical problems in engineering applications. In this work a brief introduction of the LBGK method is given and a new boundary condition is proposed for the cardiovascular domain. This enables the method to support elastic walls in two and three spatial dimensions for simulating blood flow in elastic vessels. The method is designed to be used on geometric data obtained from magnetic resonance angiography without the need of generating parameterized surfaces. The flow field is calculated in an arbitrary geometry revealing characteristic flow patterns and geometrical changes of the arterial walls for different time dependent input contours of pressure and flow. For steady flow the results are compared to the predictions of the model proposed by Y. C. Fung which is an extension of Poiseuille's theory. The results are very promising for relevant Reynolds and Womersley numbers, consequently very useful in medical simulation applications.