Abstract
Computational cardiovascular flow analysis can provide valuable information to medical doctors in a wide range of patientspecific cases, including cerebral aneurysms, aortas and heart valves. The computational challenges faced in this class of flow analyses also have a wide range. They include 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 the blood and the cardiovascular structure. Many of these challenges have been or are being addressed by the Space–Time Variational Multiscale (ST-VMS) method, Arbitrary Lagrangian–Eulerian VMS (ALE-VMS) method, and the VMS-based Immersogeometric Analysis (IMGA-VMS), which serve as the core computational methods, and the special methods used in combination with them. We provide an overview of the core and special methods and present examples of challenging computations carried out with these methods, including aorta and heart valve flow analyses. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium provided the original work is properly cited.
Highlights
Many agree that computational cardiovascular ow analysis can provide surgeons and medical doctors valuable information in a wide range of patient-specic cases, including cerebral aneurysms, treatment of cerebral aneurysms, aortas and heart valves
The task becomes even more challenging for arteries with complex geometries, such as the aorta. Many of these challenges have been or are being addressed by the SpaceTime Variational Multiscale (ST-VMS) method [6], Arbitrary LagrangianEulerian VMS (ALE-VMS) method [7], and the VMS-based Immersogeometric Analysis (IMGA-VMS) [4, 8], which serve as the core computational methods, and the special methods used in combination with them
The special methods used in combination with the ST-VMS include the ST Slip Interface (STSI) method [9, 10], ST Topology Change (STTC) [11, 12] method, ST Isogeometric Analysis (ST-IGA) [6, 13, 14], integration of these methods, a general-purpose NURBS mesh generation method for complex geometries [15, 16], and methods for estimating the zerostress state (ZSS) of the artery [1720]
Summary
Many agree that computational cardiovascular ow analysis can provide surgeons and medical doctors valuable information in a wide range of patient-specic cases, including cerebral aneurysms (see, e.g., [1]), treatment of cerebral aneurysms (see, e.g., [2]), aortas (see, e.g., [3]) and heart valves (see, e.g., [4, 5]). The computational challenges faced in this class of ow analyses have a wide range, many quite formidable They include highly-unsteady ows and complex cardiovascular geometries. The special methods used in combination with the ST-VMS include the ST Slip Interface (STSI) method [9, 10], ST Topology Change (STTC) [11, 12] method, ST Isogeometric Analysis (ST-IGA) [6, 13, 14], integration of these methods, a general-purpose NURBS mesh generation method for complex geometries [15, 16], and methods for estimating the ZSS of the artery [1720]. A divergence-free velocity eld u0(x) is specied as the initial condition
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