As a step towards addressing a scarcity of references on this topic, we compared the Eulerian and Lagrangian Computational Fluid Dynamics (CFD) approaches for the solution of free-surface and Fluid–Solid Interaction (FSI) problems. The Eulerian approach uses the Finite Element Method (FEM) to spatially discretize the Navier–Stokes equations. The free surface is handled via the volume-of-fluid (VOF) and the level-set (LS) equations; an Immersed Boundary Method (IBM) in conjunction with the Nitsche’s technique were applied to resolve the fluid–solid coupling. For the Lagrangian approach, the smoothed particle hydrodynamics (SPH) method is the meshless discretization technique of choice; no additional equations are needed to handle free-surface or FSI coupling. We compared the two approaches for a flow around cylinder. The dam break test was used to gauge the performance for free-surface flows. Lastly, the two approaches were compared on two FSI problems—one with a floating rigid body dropped into the fluid and one with an elastic gate interacting with the flow. We conclude with a discussion of the robustness, ease of model setup, and versatility of the two approaches. The Eulerian and Lagrangian solvers used in this study are open-source and available in the public domain.

Considering that granular material is second only to water in how often it is handled in practical applications, characterizing its dynamics represents a ubiquitous problem. However, studying the motion of granular material poses stiff computational challenges. The underlying question in this contribution is whether a continuum representation of the granular material, established in the framework of the smoothed particle hydrodynamics (SPH) method, can provide a good proxy for the fully resolved granular dynamics solution. To this end, two approaches described herein were implemented to run on graphics processing unit (GPU) cards to solve the three-dimensional (3D) dynamics of the granular material via two solution methods: a discrete one, and a continuum one. The study concentrates on the case when the granular material is packed but shows fluid-like behavior under large strains. On the one hand, we solve the Newton–Euler equations of motion to fully resolve the motion of the granular system. On the other hand, we solve the Navier–Stokes equations to describe the evolution of the granular material when treated as a homogenized continuum. To demonstrate the similarities and differences between the multibody and fluid dynamics, we consider three representative problems: (i) a compressibility test (highlighting a static case); (ii) the classical dam break problem (highlighting high transients); and (iii) the dam break simulation with an obstacle (highlighting impact). These experiments provide insights into conditions under which one can expect similar macroscale behavior from multibody and fluid dynamics systems governed by manifestly different equations of motion and solved by vastly different numerical solution methods. The models and simulation platform used are publicly available and part of an open source code called Chrono. Timing results are reported to gauge the efficiency gains associated with treating the granular material as a continuum.

The collagen fibres in the superficial layer of tibiofemoral articular cartilage exhibit distinct patterns in orientation revealed by split lines. In this study, we introduce a simulation framework to predict cartilage surface loading during walking to investigate if split line orientations correspond with principal strain directions in the cartilage surface. The two-step framework uses a multibody musculoskeletal model to predict tibiofemoral kinematics which are then imposed on a deformable model to predict surface strains. The deformable model uses absolute nodal coordinate formulation (ANCF) shell elements to represent the articular surface and a system of spring-dampers and internal pressure to represent the underlying cartilage. Simulations were performed to predict surface strains due to internal pressure, loading induced by walking, and the combination of both loading due to pressure and walking. Peak femoral and tibial cartilage deflections were slightly greater than 1 mm during simulated walking. First principal strain magnitudes within the cartilage surface ranged up to 3%. Time-averaged first principal strains agreed best with split line maps from the literature when surface loading due to internal cartilage pressure was included. This result suggests there may be a connection between pressure-induced surface strain patterns and the collagen fibre orientation patterns that emerge.