Computational Cardiovascular Analysis with the Variational Multiscale Methods and Isogeometric Discretization

Thomas J.R. Hughes*, Kenji Takizawa, Yuri Bazilevs, Tayfun E. Tezduyar, Ming Chen Hsu

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingChapter

14 Citations (Scopus)


Computational cardiovascular analysis can provide valuable information to cardiologists and cardiovascular surgeons on a patient-specific basis. There are many computational challenges that need to be faced in this class of flow analyses. They include highly unsteady flows, complex cardiovascular geometries, moving boundaries and interfaces, such as the motion of the heart valve leaflets, contact between moving solid surfaces, such as the contact between the leaflets, and the fluid–structure interaction between blood and cardiovascular structure. Many of these challenges have been or are being addressed by the Space–Time Variational Multiscale (ST-VMS) method, the Arbitrary Lagrangian–Eulerian VMS (ALE-VMS) method, and VMS-based immersogeometric analysis (IMGA-VMS), which serve as the core computational methods, and other special methods used in combination with them. We provide an overview of these methods and present examples of challenging computations carried out with them, including aortic and heart valve flow analyses. We also point out that these methods are general computational fluid dynamics techniques and have broad applicability to a wide range of other areas of science and engineering.

Original languageEnglish
Title of host publicationModeling and Simulation in Science, Engineering and Technology
Number of pages43
Publication statusPublished - 2020

Publication series

NameModeling and Simulation in Science, Engineering and Technology
ISSN (Print)2164-3679
ISSN (Electronic)2164-3725

ASJC Scopus subject areas

  • Modelling and Simulation
  • Engineering(all)
  • Fluid Flow and Transfer Processes
  • Computational Mathematics


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