Turbulence Generation and Left Ventricular Hemodynamics Elucidated Through Flow Decomposition
Time: Fri 2026-01-30 11.00
Location: D2, Lindstedtsvägen 5, Stockholm
Video link: https://kth-se.zoom.us/j/68657960472
Language: English
Subject area: Computer Science
Doctoral student: Joel Kronborg , Beräkningsvetenskap och beräkningsteknik (CST)
Opponent: Professor Dominik Obrist, University of Bern
Supervisor: Professor Johan Hoffman, Beräkningsvetenskap och beräkningsteknik (CST)
QC 20251218
Abstract
In recent years, the triple decomposition of the velocity gradient tensor has emerged as a novel vortex identification method in fluid flows. Although early algorithms for computing it were limited by an incomplete physical interpretation of the underlying mathematics, the decomposition has the potential to contribute to more than just vortex identification, such as shear estimation in blood flow and analysis of turbulence generation.
An attractive feature of the triple decomposition is its ability to give a rotation measure uncontaminated by shear, something that many established methods fail to do. However, several different algorithms have been proposed for computing it, and not all of them yield the same results. Here, advances are presented not only in explaining this non-uniqueness and motivating a unified and simplified approach for computing the triple decomposition, but in widening the scope of its applications as well.
In blood flow, shear is an important parameter that, if sustained at a high level, may contribute to platelet activation and subsequent thrombosis events such as stroke or myocardial infarction. Simulations are presented here of the intraventricular blood flow in the left ventricle of a human heart, both using a simplified model of the mitral valve to simulate transcatheter edge-to-edge repair, and introducing a novel arbitrary Lagrangian-Eulerian fluid-structure interaction model of the mitral valve. The triple decomposition is demonstrated to outperform the established von Mises-like scalar shear stress, which is shown to be contaminated by strain.
A mathematical stability analysis of the shear, strain and rotation components from the triple decomposition is also used to motivate a novel process in turbulence generation. In a simulation of two adjacent vortices interacting to develop turbulent flow, a zig-zag pattern is identified as a mechanism that rearranges small-scale secondary vortices to transfer energy to larger scales, contributing to the formation of a turbulent energy spectrum.
The results presented in this thesis contribute not only to better understanding and more straightforward computation of the triple decomposition, but also demonstrate its usefulness in improving analysis of potentially adverse shear in blood flow, as well as of fundamental aspects of turbulence generation.