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The technique of identifying Lagrangian Coherent Structures (LCSs) has emerged as a powerful tool for studying incompressible flows. Yet, the discrepancies arising from incompressibility assumptions often compromise the accuracy of LCSs constructed using Lagrangian particle methods. In this study, we introduce a modified framework to compute Finite-Time Lyapunov Exponents (FTLEs), addressing the misalignment between the fully incompressible assumption of LCS theory and the inherent incompressibility loss in simulations of particle methods. We begin by examining the correlation between the minimum and maximum FTLEs. By incorporating the deformation gradient and Cauchy-Green strain tensor which account for the time-advancing errors of incompressibility based on continuum theory, we enhance the computational accuracy of FTLEs. Moreover, we introduce the modified FTLE algorithm to the incompressible particle-in-cell (PIC) method for resolving free surface flows and fluid-structure interaction problems. Finally, numerical examples including the Tayler-Green vortices, water sloshing with baffles, an eccentric box sinking in water, and three-dimensional shear-driven cavity problems with high Reynolds numbers are tested to validate the effectiveness of the modified FTLE algorithm and the improved LCSs. These results demonstrate that the proposed modification scheme adeptly counteracts the errors caused by incompressibility loss, enabling accurate computation of FTLEs and detection of LCSs. [ABSTRACT FROM AUTHOR]

In recent years, the investigations on Lagrangian Coherent Structures (LCS) in complex flows have attracted increasing attention due to their ability to accurately describe flow field details. In this study, we propose a novel and accurate numerical technique based on the Lagrangian–Eulerian Stabilized Collocation Method (LESCM) for computing the Finite Time Lyapunov Exponents (FTLEs), which is essential for extracting LCSs in viscous incompressible flows. LESCM, previously employed for simulating fluid–structure interaction problems, was developed based on the Material Point Method (MPM). The hybrid Lagrangian–Eulerian​ description in LESCM enables explicit tracking of fluid flow trajectories throughout the simulation and direct evaluation of the FTLE field. Furthermore. The errors in FTLEs caused by the Particle Shifting Technique (PST) are completely avoided due to the Eulerian characteristic of LESCM as the deformation gradient is calculated based on fixed Eulerian nodes rather than fluid particles with unphysical shifting. Consequently, the novel technique based on LESCM surpasses the accuracy of pure Lagrangian particle methods and provides an accurate way of detecting complex LCSs in flow fields. Additionally, By harnessing the remarkable efficiency of LESCM, MATLAB can now handle up to 16 million particles with ease, eliminating the need for parallel computation techniques. Several numerical examples, such as 2D Taylor-Green​ vortices, flow passing a circular cylinder and a 3-dimensional shear driven cavity problem, have been tested to demonstrate the effectiveness of this novel approach under various conditions. [ABSTRACT FROM AUTHOR]

Patient-specific simulation of the fluid–structure interaction (FSI) problems in cardiovascular systems plays an increasingly important role in fundamental research and clinical applications. However, modeling such problems is challenging, as they often involve non-trivial structural deformation, morphing flow domains, and complex interfaces. In this paper, we develop an incompressible SPH-total Lagrangian SPH (ISPH-TLSPH) framework well-adapted to cardiovascular FSI simulations. The matrix-free iterative ISPH method is used to simulate the hemodynamics and the stabilized TLSPH is used to simulate the dynamics of blood vessels. We propose a novel FSI coupling strategy to couple the ISPH with TLSPH, conforming to strict interface matching conditions. Moreover, we accurately incorporate the lumped parameter (0D) models into the 3D SPH framework to simulate the physiological effects of downstream vascular beds. Lastly, graphics processing unit (GPU) parallelization techniques are implemented in our framework to improve efficiency. The developed framework is first validated by investigating the pulse wave propagation in straight vessels under different boundary conditions. Then the FSI processes in the blood vessel with stenosis and the patient-specific aorta are modeled and investigated. The simulation results show that our framework is effective and efficient for the simulations of patient-specific blood vessels. • A framework that couples the matrix-free iterative ISPH with TLSPH is developed. • A novel coupling strategy for fluid–structure interaction is proposed. • A 3D-0D coupled model is introduced to the SPH framework. • GPU parallelization is implemented for accelerating SPH computations. [ABSTRACT FROM AUTHOR]

As a typical fluid–structure interaction (FSI) problem, water entry involves violent fluid flows and changing free surfaces, which presents great challenges for numerical modeling. Smoothed Particle Hydrodynamics (SPH) is a Lagrangian particle method that has natural advantages in modeling free surfaces and moving interfaces. However, SPH is computationally expensive due to the search of particle–particle interactions, and it causes great difficulties for performing large-scale simulations of 3D FSI problems. In this work, we present an accelerated SPH framework based on the Graphics Processing Unit (GPU) techniques to study water entry problems. The multi-threading programmed by Compute Unified Device Architecture (CUDA) is applied to enhance the computational performance in terms of efficiency and scale. Compared to the Single-CPU-based strategy, the newly presented GPU-accelerated SPH method is computationally more efficient with a speedup over hundreds times and enables a larger memory available for large-scale simulations of around ten million particles for three-dimensional cases. With the GPU-accelerated SPH method, the 3D water entry of a circular cylinder is investigated with some kinematic and dynamic characteristics explained. The results demonstrate that the rotational characteristic of a 3D cylinder in water entry is related to the dimensionless number γ defined as the ratio of the initial inclination angle to the initial velocity angle. The rotation of a cylinder changes from anticlockwise to clockwise with the increase in γ. A transition value of γ exists between the anticlockwise to clockwise rotation, which focuses on the range from 1.0 to 6.0. Meanwhile, the water entry of a 3D circular cylinder leads to a violent impact on the bottom of the cylinder, which causes a peak value of pressure being a maximum value at the early stage of the water entry. It is also indicated that the selection of the initial inclination angle has a great effect on the maximum pressure. • A GPU-accelerated SPH method for fluid–structure interaction problems is developed. • The GPU-accelerated SPH method can greatly improve the computational ability compared to CPU-based SPH. • The water entry characteristics of a 3D cylinder relate to the ratio of the initial inclination angle to velocity angle. • A cross-region that the trajectory of the centroid always passes through is determined by the initial velocity angle. [ABSTRACT FROM AUTHOR]

Existing studies of fluid-structure interaction (FSI) in ocean engineering mainly focus on the interaction between Newtonian fluids and structure. The FSI problems involving non-Newtonian fluids, especially viscoplastic fluids, have rarely been studied while the inherent dynamic behavior is not clear. In this paper, an immersed boundary-lattice Boltzmann method (IB-LBM) is developed for numerical investigations on FSI problems involving viscoplastic fluids. The present IB-LBM is integrated with a hybrid multiple relaxation times (MRT) scheme where different diagonal relaxation matrices are used for modeling Newtonian and non-Newtonian fluids, and are combined in a hybrid manner using a step function to achieve smooth transition for Newtonian to non-Newtonian fluid behavior at the FSI area. Four benchmark problems are used to validate the IB-LBM with hybrid MRT scheme. It is demonstrated that the numerical model can avoid numerical instability when modeling viscoplastic fluid flow and reduce the numerical boundary slip in the IB-LBM. The numerical model is further used to study the viscoplastic fluid flow around a fixed and moving cylinder (or particle). We show that the present IB-LBM with the hybrid MRT scheme is effective in modeling FSI involving viscoplastic fluids while the obtained phenomena are quite different from those with Newtonian fluids. [ABSTRACT FROM AUTHOR]