Arbitrary Lagrangian Eulerian Simulations Research Articles

Obtaining smooth mesh transitions using vertex optimization

AbstractMesh optimization has proven to be an effective way to improve mesh quality for arbitrary Lagrangian Eulerian (ALE) simulations. To date, however, most of the focus has been on improving the geometric shape of individual elements, and these methods often do not result in smooth transitions in element size or aspect ratio across groups of elements. We present an extension to the mean ratio optimization that addresses this problem and yields smooth transitions within regions and across regions in the ALE simulation. While this method is presented in the context of ALE simulations, it is applicable to a wider set of applications that require mesh improvement, including the mesh generation process. Published in 2007 by John Wiley & Sons, Ltd.

Cylindrical 2D ALE simulations of laser interactions with flyer targets

We have developed 2D Arbitrary Lagrangian Eulerian (ALE) code in the cylindrical r-z geometry. The ALE method overcomes problems with Lagrangian moving mesh distortion by mesh smoothing and conservative quantities remapping from Lagrangian mesh to smoothed one. The flyer target experiments [1, 2] performed at the Prague PALS laser facility are simulated by the developed code. The thin flyer disc is irradiated by intense laser beam and ablatively accelerated up to very high velocities (till 150km/s) against a solid target. The high velocity impact of disc flyer on the target creates a crater. The high velocity impact simulations cannot be accomplished by standard Lagrangian code without the ALE method. The simulation results for several laser energies in 120–390 J range and laser basic and third harmonics compare reasonably with experimental data which include disc flyer impact velocities and crates sizes.

Modeling NIF experimental designs with adaptive mesh refinement and Lagrangian hydrodynamics

Incorporation of adaptive mesh refinement (AMR) into Lagrangian hydrodynamics algorithms allows for the creation of a highly powerful simulation tool effective for complex target designs with three-dimensional structure. We are developing an advanced modeling tool that includes AMR and traditional arbitrary Lagrangian-Eulerian (ALE) techniques. Our goal is the accurate prediction of vaporization, disintegration and fragmentation in National Ignition Facility (NIF) experimental target elements. Although our focus is on minimizing the generation of shrapnel in target designs and protecting the optics, the general techniques are applicable to modern advanced targets that include three-dimensional effects such as those associated with capsule fill tubes. Several essential computations in ordinary radiation hydrodynamics need to be redesigned in order to allow for AMR to work well with ALE, including algorithms associated with radiation transport. Additionally, for our goal of predicting fragmentation, we include elastic/plastic flow into our computations. We discuss the integration of these effects into a new ALE-AMR simulation code. Applications of this newly developed modeling tool as well as traditional ALE simulations in two and three dimensions are applied to NIF early-light target designs.

ALE simulations of high-velocity impact problem

We describe here our newly developed ALE code on 2D quadrilaterals. The code is employed here in the numerical simulations of the erater formation during impact of small accelerated object on bulk target. The simulation of the high-velocity impact problem by the Lagrangian hydrodynamical codes leads in later stages to severe distortion of the Lagrangian grid which prevents continuation of computation. Such situations can however be treated by the Arbitrary Lagrangian Eulerian (ALE) method. In order to maintain the grid quality, the ALE method applies grid smoothing regularly after several time steps of Lagrangian computation. After changing the grid, the conservative quantities have to be conservatively remapped from the old grid to the new, better one. After remapping, Lagrangian computation can continue.

Untangling of 2D meshes in ALE simulations

A procedure is presented to untangle unstructured 2D meshes containing inverted elements by node repositioning. The inverted elements may result from node movement in Arbitrary Lagrangian–Eulerian (ALE) simulations of continuum mechanics problems with large shear deformation such as fluid flow and metal forming. Meshes with inverted elements may also be created due to the limitations of mesh generation algorithms particularly for non-simplicial mesh generation. The untangling procedure uses a combination of direct node placement based on geometric computation of the feasible set, and node repositioning driven by numerical optimization of an objective function that achieves its minimum on a valid mesh. It is shown that a combination of the feasible set, based method and the optimization method achieves the best results in untangling complex 2D meshes. Preliminary results are also presented for untangling of 3D unstructured meshes by the same approach.

Injection/suction boundary conditions for fluid–structure interaction simulations in incompressible flow

AbstractThis paper presents the analysis of injection/suction boundary conditions in the context of the fluid–structure interactions simulation of the incompressible turbulent flow.First, the equations used in the modelling of the fluid and the structure are presented, as well as the numerical methods used in the corresponding solvers. Injection/suction boundary conditions are then presented with details of different implementation alternatives. Arbitrary Lagrangian–Eulerian (ALE) approach was also implemented in order to test the injection/suction boundary conditions.Numerical tests are performed where injection/suction boundary conditions are compared to ALE simulations. These tests include forced movement of the structure and two‐degrees‐of‐freedom structure model simulations. Copyright © 2002 John Wiley & Sons, Ltd.

Large eddy simulation and ALE mesh motion in Rayleigh–Taylor instability simulation

Many large eddy simulation (LES) techniques have been developed for stationary computational meshes. This study applies a single equation LES to Arbitrary Lagrangian–Eulerian (ALE) simulations of Rayleigh–Taylor instability and investigates its effects. Behavior of LES is similar for Eulerian and ALE simulations for the test problem studied. However, the motion of the mesh can be tied to the subgrid scale model in the form of a relaxation weight based on subgrid scale energy. This increases mesh resolution in areas of high subgrid scale energy.

A study of ALE simulations of Rayleigh–Taylor instability

This paper investigates the use of an Arbitrary Lagrangian–Eulerian (ALE) technique on a single-mode Rayleigh–Taylor instability simulation in two dimensions. A finite volume approach on a simply connected quadrilateral grid is used. The effect of various modifications in the ALE method on instability growth, energy balance, and mesh distortion are investigated. It is shown that ALE mesh motion can be used to improve single mode Rayleigh–Taylor Instability simulations.