A deformation-dependent visualization scheme in the framework of the Material Point Method

Abstract

Recent advancements in the Material Point Method (MPM) have significantly improved the simulation of fluid–structure interaction (FSI) problems. However, regardless of the significant advantages of FSI simulation that the MPM can offer, further improvements in flow visualization are essential for analyzing a complicated fluid field. This article presents an innovative approach that integrates Lagrangian Coherent Structures (LCS) with both weakly compressible MPM (WCMPM) and incompressible MPM (iMPM) to improve the identification and analysis of flow structures in complicated FSI problems. The MPM excels in tracking material motion and accurately computing deformation gradients, which is a crucial step for the extraction of the LCS. This combination renders the MPM an ideal complement to the LCS technique, facilitating a detailed examination of complex vortex patterns within flow fields. Unlike traditional particle methods such as Smoothed Particle Hydrodynamics, the MPM boasts a distinct advantage in accuracy for calculating the deformation gradients, which can mitigate errors associated with particle shifting techniques as the deformation gradients are calculated based on the velocities on the background grid. The utility of the LCS visualization within the MPM framework is demonstrated through various numerical experiments, which include the analysis of a water–snow interaction problem, a viscous wake generated by an inclined ellipse, models of fish-like swimming, and liquid sloshing with baffles under different conditions. These studies highlight the ability of the method to offer detailed insights into flow dynamics, confirming the superior capability of the MPM in capturing the complex characteristics of LCSs in viscous incompressible flow fields.