Keywords: contact, impact, free surface, multi-physics, parallel.

For collision problems, where a projectile penetrates a structure, tracking the interface between one material and another becomes very complex. The conventional approaches to the analysis of collision processes involve a Lagrangian-Lagrangian contact driven methodology. The solution time for such simulations is very substantial and, frequently, the scalability of its parallel implementation is inhibited by the contact analysis component of the calculations. This paper describes a 'two-fluid' Eulerian approach to high speed impact between solid structures, where the objective is to overcome the problems of penetration and re-meshing, and so retain the parallel scalability afforded by conventional CFD applications.

Since the early 1970s there has been a significant research effort on the development of numerical techniques and codes to address projectile-target impact problems. Understandably, after the events of 11th September 2001 (9/11), there has been a significant rise in interest in assessing the security of structures subject to collision with high speed projectiles. This event highlighted the importance of being able to capture a range of other concurrent phenomena, especially if the projectile contains a fluid, e.g. has a fuel load. So that in addition to dynamic structural interaction and the dynamic response, the subsequent combustion, heat transfer, softening and possibly any phase change also need to be accounted for.

Collision is an example of the more generic contact problem where, by definition, there will be penetration of the small, often fast moving, projectile into the larger target. Conventional FE Lagrangian modelling [1] of contact between two bodies requires the definition of a "contact-pair", where the surface of one body is taken as the contact surface and the other is taken as the target surface. This approach has been widely used in FE modelling of contact problems, see [1], however, it requires periodic re-meshing to overcome unacceptable element distortion, associated with penetration, which is expensive in CPU time.

In this work the solution strategy is as follows. Prior to collision with the target, the projectile is assumed to move through a host fluid domain e.g. air or water, as a very viscous 'pseudo-fluid'. Thus the projectile, the host fluid and the target sub-domains are all assumed to be components of a single Eulerian 'pseudo-fluid' throughout the whole domain. In terms of the CFD approach, there are multiple free surfaces involved, since surfaces between each of the material types must be tracked. In this work these material interfaces are modelled using a conventional VOF-like free surface CFD technique [2,3], which has the advantage of solving for flow throughout the whole 'pseudo-fluid' domain and so can account for each and all of the materials.

The model is implemented within the three dimensional multi-physics solver, PHYSICA [3], which runs in parallel with a good degree of scalability [4]. Three dimensional fluid flow and various other physics algorithms are approximated using element-centred, Finite Volume Unstructured Mesh techniques on a collocated mesh. This code also has a Lagrangian solid mechanics solver which has been closely coupled into the flow solver for fluid-structure interaction problems [5]. Procedures originally developed to capture the transition from a liquid to a solid phase in solidification problems [6] are adapted here to identify where the material begins to behave as either a 'pseudo-fluid' or a solid. A mixed Eulerian Lagrangian procedure is then used to calculate the appropriate state of the material on an element by element basis.

1

Swanson Analysis Systems, Inc., P.O. Box 65, Johnson Road, Houston, PA 154342-0065, ANSYS

2

Jun, L and Spalding, D.B. Numerical simulation of flows with moving interfaces, Physico-Chemical Hydrodynamics, 1988, 10, pp 625-637

3

PHYSICA, http:/www.physica.co.uk

4

McManus, K., Williams, A.J., Cross, M., Croft, T.N. and Walshaw, C. "Assessing the scalability of multi-physics tools for modelling solidification melting processes on parallel clusters", International Journal of High Performance Computing Applications. 2005, 19, 1, pp 1- 27. doi:10.1177/1094342005051198

5

Slone, A.K., A Finite Volume Unstructured Mesh Approach to Dynamic Fluid-Structure Interaction between Fluids and Linear Elastic Solids, PhD thesis, The University of Greenwich, 2000

6

V.R. Voller, V.R. and Swaminathan, C.R. "General source-based method for solidification phase change". Numerical Heat Transfer B 19, (1991),pp 175-189 doi:10.1080/10407799108944962

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