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Abstract and Applied Analysis
Volume 2014 (2014), Article ID 549189, 8 pages
http://dx.doi.org/10.1155/2014/549189
Review Article

Some Numerical Approaches to Solve Fluid Structure Interaction Problems in Blood Flow

Department of Mathematical Sciences, Faculty of Science, Universiti Teknologi Malaysia UTM, 81310 Johor Bahru, Johor Darul Takzim, Malaysia

Received 4 October 2013; Accepted 12 January 2014; Published 23 February 2014

Academic Editor: Mohamed Fathy El-Amin

Copyright © 2014 Aik Ying Tang and Norsarahaida Amin. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Some numerical approaches to solve fluid structure interaction problems in blood flow are reviewed. Fluid structure interaction is the interaction between a deformable structure with either an internal or external flow. A discussion on why the compliant artery associated with fluid structure interaction should be taken into consideration in favor of the rigid wall model being included. However, only the Newtonian model of blood is assumed, while various structure models which include, amongst others, generalized string models and linearly viscoelastic Koiter shell model that give a more realistic representation of the vessel walls compared to the rigid structure are presented. Since there exists a strong added mass effect due to the comparable densities of blood and the vessel wall, the numerical approaches to overcome the added mass effect are discussed according to the partitioned and monolithic classifications, where the deficiencies of each approach are highlighted. Improved numerical methods which are more stable and offer less computational cost such as the semi-implicit, kinematic splitting, and the geometrical multiscale approach are summarized, and, finally, an appropriate structure and numerical scheme to tackle fluid structure interaction problems are proposed.