Abstract This study presents an investigation of the plunge stage in joining AZ31B magnesium alloy with friction stir welding using two different 3D finite element models based on Arbitrary Lagrangian–Eulerian formulation and Coupled Eulerian–Lagrangian formulation. The investigations are made ABAQUS program. Johnson–Cook plastic material law Coulomb used both models. Models compared terms temp...

We perform a systematic multiscale analysis for the 2-D incompressible Euler equation with rapidly oscillating initial data using a Lagrangian approach. The Lagrangian formulation enables us to capture the propagation of the multiscale solution in a natural way. By making an appropriate multiscale expansion in the vorticity-stream function formulation, we derive a well-posed homogenized equatio...

A new approach to cosmological hydrodynamics is discussed which is based on a moving, quasi-Lagrangian mesh. The softened Lagrangian hydrodynamics (SLH) method utilizes a high resolution Lagrangian hydrodynamic code combined with a low resolution Eulerian solver to deal with severe mesh distortions. Most of the volume of a simulation is treated with the Lagrangian code and only in sites where t...

We study the hp version of three families of Eulerian-Lagrangian mixed discontinuous finite element (MDFE) methods for the numerical solution of advectiondiffusion problems. These methods are based on a space-time mixed formulation of the advection-diffusion problems. In space, they use discontinuous finite elements, and in time they approximately follow the Lagrangian flow paths (i.e., the hyp...

Potentially this paper contains some results that may be of interest to NPG, but not in its present form. The main issue is that the authors describe the method of Lagrangian descriptors in a variety of misleading and wrong ways, and they also have neglected to mention a large amount of relevant literature. The authors develop a new Lagrangian descriptor based on integrating the magnitude of th...

The issue of the parameterization of small-scale dynamics is addressed in the context of passive-scalar turbulence. The basic idea of our strategy is to identify dynamical equations for the coarse-grained scalar dynamics starting from closed equations for two-point statistical indicators. With the aim of performing a fully-analytical study, the Kraichnan advection model is considered. The white...

We report the detailed multi-scale and multi-directional geometric study of both evolving Lagrangian and instantaneous Eulerian structures in turbulent channel flow at low and moderate Reynolds numbers. The Lagrangian structures (material surfaces) are obtained by tracking the Lagrangian scalar field, and Eulerian structures are extracted from the swirling strength field at a time instant. The ...