ALEGRA is a multi-material, arbitrary-Lagrangian-Eulerian (ALE) code for solid dynamics being developed by the Computational Physics Research and Development Department at Sandia +tionat Laboratories. It combines the features of modem Eulerian shock codes, such as CTH, with modem Lagrangian structural analysis codes. With the ALE algorithm, the mesh can be stationary (Eulerian) with the materia...

We study the observability of one and two point vortex flow from one or two Eulerian or Lagrangian observations. By observability we mean the ability to determine the locations and strengths of the vortices from the time history of the observations. An Eulerian observation is a measurement of the velocity of the flow at a fixed point in the domain of the flow. A Lagrangian observation is the me...

The gradient-flow dynamics of an arbitrary geometric quantity is derived using a generalization of Darcy’s Law. We consider flows in both Lagrangian and Eulerian formulations. The Lagrangian formulation includes a dissipative modification of fluid mechanics. Eulerian equations for self-organization of scalars, 1-forms and 2-forms are shown to reduce to nonlocal characteristic equations. We iden...

Preferential concentration of inertial particles in turbulence is studied numerically by evaluating the Lagrangian compressibility of the particle velocity field using the "full Lagrangian method." This is compared with the "mesoscopic Eulerian particle velocity field" both in a direct numerical simulation of turbulence and in a synthetic flow field. We demonstrate that the Lagrangian method, i...

1.1. Eulerian and Lagrangian coordinates. Let us begin with Eulerian and Lagrangian coordinates. The Eulerian coordinate (x, t) is the physical space plus time. The Eulerian description of the flow is to describe the flow using quantities as a function of a spatial location x and time t, e.g. the flow velocity u(x, t). This can be visualized by sitting on the bank of a river and watching the wa...

Three-dimensional particle tracking velocimetry (3D-PTV) measurements have provided accurate Eulerian and Lagrangian high-order statistics of velocity and acceleration fluctuations and correlations at Reynolds number 10,300, based on the bulk velocity and the pipe diameter. Spatial resolution required in the analysis method and number of correlation samples required for Lagrangian and Eulerian ...

Two stages gas guns are used for various purposes, particularly for mechanical characterization of materials at high rate of deformations. The performance of a two stages gas gun is studied in this work using the theory of the two-stage gas gun proposed by Rajesh, numerical simulation using combined Eulerian/ Lagrangian elements in Autodyna commercial code and experiment using a two stage gas g...

We provide methods of computing multivalued solutions to the Euler-Poisson system and test them in the context of a klystron amplifier. An Eulerian formulation capable of computing multivalued solutions is derived from a kinetic description of the Euler-Poisson system and a moment closure. The system of the moment equations may be closed due to the special structure of the solution in phase spa...

ALEGRA is a multi-material, arbitrary-Lagrangian-Eulerian (ALE) code for solid dynamics being developed by the Computational Physics Research and Development Department at Sandia National Laboratories. It combines the features of modern Eulerian shock codes, such as CTH, with modern Lagrangian structural analysis codes. With the ALE algorithm, the mesh can be stationary (Eulerian) with the mate...

A coordinate independent derivation of the Eulerian and Lagrangian strain tensors of finite deformation theory is given based on the parallel propagator, the world function, and the displacement vector field as a three-point tensor. The derivation explicitly shows that the Eulerian and Lagrangian strain tensors are two-point tensors, each a function of both the spatial and material coordinates....