ALEGRA is an arbitrary Lagrangian-Eulerian (multiphysics) computer code developed at Sandia National Laboratories since 1990. The code contains a variety of physics options including magnetics, radiation, and multimaterial flow. The code has been developed for nearly two decades, but recent work has dramatically improved the code's accuracy and robustness. These improvements include techniques applied to the basic Lagrangian differencing, artificial viscosity and the remap step of the method including an important improvement in the basic conservation of energy in the scheme. We will discuss the various algorithmic improvements and their impact on the results for important applications. Included in these applications are magnetic implosions, ceramic fracture modeling, and electromagnetic launch.

SUMMARYThis paper presents a detailed multi-methods comparison of the spatial errors associated with ÿnite difference, ÿnite element and ÿnite volume semi-discretizations of the scalar advection-di usion equation. The errors are reported in terms of non-dimensional phase and group speed, discrete di usivity, artiÿcial di usivity, and grid-induced anisotropy. It is demonstrated that Fourier analysis provides an automatic process for separating the discrete advective operator into its symmetric and skew-symmetric components and characterizing the spectral behaviour of each operator. For each of the numerical methods considered, asymptotic truncation error and resolution estimates are presented for the limiting cases of pure advection and pure di usion. It is demonstrated that streamline upwind Petrov-Galerkin and its control-volume ÿnite element analogue, the streamline upwind control-volume method, produce both an artiÿcial di usivity and a concomitant phase speed adjustment in addition to the usual semi-discrete artifacts observed in the phase speed, group speed and di usivity. The Galerkin ÿnite element method and its streamline upwind derivatives are shown to exhibit super-convergent behaviour in terms of phase and group speed when a consistent mass matrix is used in the formulation. In contrast, the CVFEM method and its streamline upwind derivatives yield strictly second-order behaviour. In Part II of this paper, we consider two-dimensional semi-discretizations of the advection-di usion equation and also assess the a ects of grid-induced anisotropy observed in the non-dimensional phase speed, and the discrete and artiÿcial di usivities. Although this work can only be considered a ÿrst step in a comprehensive multimethods analysis and comparison, it serves to identify some of the relative strengths and weaknesses of multiple numerical methods in a common analysis framework. Published in 2004 by John Wiley & Sons, Ltd.

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ALEGRA is an arbitrary Lagrangian-Eulerian finite element code that emphasizes large distortion and shock propagation. This document describes the user input language for the code.

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