Chapter 1. Overview
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§1.
§2.
• Shell processor for modeling thin structural elements
• SPH (Smooth Particle Hydrodynamics) - not in general release
At present, all the above processors use explicit time integration. Libraries of material data
are included for solids, liquids, and gases (including high explosives and detonation
products).
Lagrange Processor
The Lagrange scheme in AUTODYN was derived from the method used by Wilkins (1973) in
the HEMP code. The Lagrange processor operates on a structured (I-J-K) numerical mesh
of quadrilateral (2D) or brick-type elements (3D). The vertices of the mesh move with
material flow velocity. Material remains within its initial element definition with no transport of
material from cell to cell.
Compared to the Eulerian approach, discussed below, the Lagrange formulation tends to be
faster computationally as no transport of material through the mesh needs to be calculated.
Moreover, material interfaces, free surfaces, and history dependent material behavior are
generally easier to follow in the Lagrange framework. The major disadvantage of Lagrange
is that if excessive material movement occurs, the numerical mesh may become highly
distorted leading to an inaccurate and inefficient solution. Further, this may ultimately lead to
a termination of the calculation. Rezoning the numerical mesh by remapping the distorted
solution onto a more regular mesh is one approach to alleviate the mesh distortion problem.
AUTODYN provides this capability through an interactive rezoner that allows the Lagrange
processor to successfully model many problems that would normally require an Eulerian
solution (Itoh & Cowler 1987). Other techniques, such as erosion, are also standardly
available in AUTODYN and can be used to further extend the Lagrange formulation to highly
distorted phenomenon.
Because of its inherent efficiency, the Lagrange processor is typically used whenever the
deformations and boundary conditions permit. However, large deformations and true fluid
and gas dynamics are generally more practically handled with an Eulerian approach.
Euler Processors
The original first-order approach scheme in AUTODYN is based upon the method developed
by Hancock (1976). Two different higher order Eulerian schemes have been introduced into
AUTODYN (1995). The Godunov multi-material with strength higher order processor was
developed following techniques initially developed by van Leer (1977, 1979). The FCT
higher order single material Euler processor is based on the algorithm by Zalesak (J. Comp.
Physics, 31, 335-362, 1979) which is itself based on the earlier operator split algorithms by
Boris & Book (Methods in Computational Physics, 16, 85-129, 1976). The various Euler
processors are currently directed at different needs. The first-order scheme is used for fluid-
structure, gas-structure interaction problems. The multi-material Godunov second-order
scheme is used for purely fluid and gas dynamic calculations or highly distorted structural
materials. The FCT scheme is used for single material gas dynamic problems. Neither
higher order scheme, as of this writing, includes coupled capability.