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High rate continuum modeling mesh reduction methodologies and advanced applications

E. L. Baker, D. Pfau, J. M. Pincay, T. Vuong & K. W. Ng U.S. Army Armament Research, Development and Engineering Center Picatinny, USA

Abstract

A variety of mesh reduction methodologies (MRM) have been developed for use

technique has been implemented for use in the CTH high rate Eulerian finite difference model. This new implementation allows increased rectilinear mesh refinement in localized areas of interest. We have applied this AMR to successfully resolve dominating physical phenomena involved in concrete wall impact modeling, as well as physical phenomena observed at the material interface of explosively welded metals. In addition, a variety of MRM relaxation algorithms have been developed for high rate continuum Arbitrary Lagrangian-Eulerian (ALE) modeling. These relaxation algorithms are now routinely used to provide the high resolution simulation of explosively produced metal jetting using the CALE computer program. Finally, a multi-mesh MRM technique has been implemented in the ALE-3D computer model. This MRM technique has been used to provide the modeling of fragment impact for the development of safer munitions. These new MRM techniques are now allowing the high rate continuum modeling of physical phenomena that was not previously simulated. Keywords: mesh reduction methodologies, high rate continuum modeling, impact physics, high explosives.

1 Introduction

High rate continuum modeling is used for the modeling of high rate events including high explosive detonation and high velocity impact. These models typically provide explicit second order integration in time and space of the

Boundary Elements and Other Mesh Reduction Methods XXVIII 111

in high rate continuum modeling. An adaptive mesh refinement (AMR)

doi:10.2495/BE06012

© 2006 WIT PressWIT Transactions on Modelling and Simulation, Vol 42, www.witpress.com, ISSN 1743-355X (on-line)

conservation equations. Due to the extreme deformations often observed, Eulerian and ALE modeling are often chosen over traditional Lagrangian methodology. As the requirements for increased problem size and increased resolution constantly push existing computational platforms to their limits, methods to reduce computational time and memory requirements can be extremely beneficial. In particular, a variety of mesh reduction methodologies (MRM) have been developed and implemented for use in high rate continuum modeling. These new MRM techniques are now being applied for the modeling of high rate physical phenomena not previously successfully modeled.

2 Eulerian adaptive mesh refinement

Adaptive mesh refinement (AMR) has been investigated as a method for improving computational resolution, reducing memory requirements and increasing computational efficiency for high rate continuum modeling by a number of researchers [1, 2, 3]. The implementation of such an adaptive mesh refinement capability has been recently completed by Sandia National Laboratories in the multi-materials high rate continuum computer model, CTH [4]. In order to achieve a practical implementation with good parallel performance, a block-based approach has been implemented with refinement and un-refinement occurring in an isotropic 2:1 manner. Crawford et al. [5] showed that practical speed-up from 3 to 10 times and at least 3 times memory requirement reductions can be achieved on multiprocessor and massively parallel platforms. His studies also indicated further improvements for larger problems. As the block refinement and un-refinement are very computationally expensive serial procedures, parallel performance of the adaptivity required that CTH use a super-cycling capability for refinement and un-refinement. In the current implementation, refinement occurs every two or three cycles and un-refinement will occur every six cycles. This is accomplished by using a two cell thick trigger region at the boundary of each block. When a refinement indicator reaches its threshold, then the adjacent block is signaled for refinement at least two cycles before the refinement is needed. Although somewhat ad-hoc in nature, the performance of this procedure has proven improved parallel efficiency, particularly when coupled with message passing consolidation and an efficient load balancing strategy. To date, the entire mesh is cycled with a single time step, determined by smallest time increment that meets stability based criteria, normally associated with the highest resolution mesh. Currently implemented refinement indicators include velocity, pressure, temperature, materials and material boundaries as indicated by mixed cells. Refinement indicator operators include absolute value, gradient magnitude and maximum difference. We have used this new capability to produce increased rectilinear mesh refinement in localized areas of interest. In particular, AMR has been used to successfully resolve physical phenomena observed at the material interface of explosively welded metals, as well as dominating physical phenomena involved in masonry wall impact modeling. An ongoing computational investigation of

112 Boundary Elements and Other Mesh Reduction Methods XXVIII


explosive cladding of Ta based materials is being conducted in support of the U.S. Army Future Combat System Durable Gun Barrels Manufacturing Technology Objective (MTO) and the Chromium Elimination SERDP program. The objective of the effort is to develop and demonstrate physics based modeling for explosive barrel cladding process design and optimization. Actual explosive welding of tantalum based liners to the inside of gun barrels is being undertaken by TPL Inc. Figures 1 and 2 present CTH calculations of the tantalum gun barrel cladding process.

Figure 1: Material plots of gun barrel cladding.

Figure 2: Material plots of gun barrel cladding in the muzzle region

displaying mesh blocks.

We have also used the new AMR routines in CTH to successfully resolve dominating physical phenomena involved in concrete wall impact modeling. In previous modeling efforts of modeling projectile penetration of concrete walls,



the steel reinforcement bars were not successfully resolved, due to the large memory requirements to resolve these relatively fine structures. The steel reinforcement bars are an important part of the physical process, as they provide both significant strengthening for the wall and a higher density material within the concrete wall that can significantly damage the projectile during the concrete wall penetration process. Figure 3 presents initial and late time plots of the projectile concrete wall penetration process. Figure 4 presents the initial state material region plot if the mesh refinement is not used. In this example, refinement indicators are used in order to refine everywhere individual volume fractions are greater than 0 (anywhere those materials exist), except for concrete. Three levels of refinement are used, with a minimum cell size of 1.6mm. In this way, the projectile and concrete reinforcement bars are highly refined, whereas the surrounding air (modeled as void) and concrete are less refined.

Figure 3: Initial and late time plots of the projectile concrete wall penetration process showing mesh blocks (dimensions in cm).

Figure 4: Initial state material region plot if the mesh refinement is not used.



3 Arbitrary Lagrange-Eulerian mesh relaxation

In addition, a variety of MRM relaxation algorithms have been developed for high rate continuum Arbitrary Lagrangian-Eulerian (ALE) modeling and implemented by R. Tipton in the CALE computer program [6]. These relaxation algorithms have been successfully used to provide high resolution simulation of explosively produced jetting. This jetting is produced in shaped charge warheads where an axisymmetric hollow metal liner, typically copper, is imploded onto the axis. The imploding metal liner undergoes an extremely high rate jetting deformation process and projects a high velocity metal jet forward. Figures 5 and 6 present material region and mesh plots of the jetting process of a shaped charge. A weighted potential algorithm [7] based on material fractions is used in the CALE program for this modeling. In this way, the higher weighted materials result in increased resolution mesh areas. This can clearly been seen in the figures.

Figure 5: Material and mesh plots of the initial shaped charge configuration.

Figure 6: Material and mesh plots of the jetting shaped charge liner.



4 Multi-mesh technique

Finally, a multi-mesh MRM technique has been developed for ALE modeling and has been implemented in the ALE-3D computer program [8, 9]. In this implementation, separate meshes can be attached to form a larger “multi-mesh configuration. This mesh reduction methodology can provide significant mesh reduction by only meshing regions of interest. We have used the MRM technique has been used to provide modeling of bullet impact for development of safer munitions. Reduced mesh sizes are achieved with required mesh resolutions, by meshing the munition that is being attacked and than using a small attached sub-mesh that included the bullet that is impacting the munition being attacked. Figure 7 presents an example bullet impact configuration in which the to mesh setup configuration is used. Figure 8 presents material plots of the resulting bullet impact response of the attacked munition.

5 Conclusions

A variety of MRM techniques have been investigated and successfully applied for high rate continuum modeling of ballistic events. In particular, Eulerian adaptive mesh refinement has been used for 2D and 3D modeling using the CTH computer program to reduce memory requirements and reduce computational times. This technique has allowed extremely resolved modeling of explosive welding of tantalum materials to steel that was not previously possible. Additionally, this MRM technique now allows the resolution of masonry wall penetration details that was not previously possible due to memory restrictions. Steel reinforcement materials have now been resolved, that are physically important to munition wall penetration process.

Figure 7: Initial bullet impact configuration showing the two mesh setup.



Figure 8: Material plots of the resulting bullet impact response.

Weighted potential algorithms have also been successfully used in shaped charge jet formation modeling to produce high resolution physics of the jet formation process. Finally, a multi-mesh technique has been used in the ALE-3D computer program to reduce memory requirements and reduce computational time required to perform bullet impact modeling in support of safer munitions development. These new MRM techniques are currently available in several advanced high rate continuum modeling programs and are now allowing the high rate continuum modeling of physical phenomena that was not previously simulated.

References

[1] Berger, M.J. & Colella, P., Local adaptive mesh refinement for shock hydrodynamics, J. Comp. Phys., 82, 64-84, 1989.

[2] Jones, B., SHAMROCK – an adaptive, multi-material hydrocode. Proc. of the International Workshop on new Models and Numerical Codes for Shock Wave Processes in Condensed Media, St. Catherines College, Oxford, UK, 15-19 September 1997.

[3] Tang, P.K & Scannapieco, A.J., Modeling cylinder test, Proc. of the Conference of the American Physical Society Topical Group on Shock Compression of Condensed Matter, Seattle, WA, USA, August 13-18, 1995, 449-452.

[4] Crawford, D.A., Adaptive mesh refinement in CTH, Proc. of the 15th U.S. Army Symposium on Solid Mechanics, Myrtle Beach, South Carolina, USA, April 12-14, 1999.

[5] Crawford, D.A., Taylor, P.A., Bell, R.L. & Hertel, E.S., Adaptive mesh refinement in the CTH shock physics hydrocode, Proc. of New Models



and Hydrocodes for Shock Wave Processes in Condensed Matter, Edinburgh, U.K., May 19-24, 2002.

[6] Tipton, R.E., CALE users manual, Lawrence Livermore National Laboratory, Oct. 1995.

[7] Winslow, A. 1963, Equipotential zoning of two dimensional meshes, LLNL Report UCRL-7312, 1963.

[8] Couch, R., Sharp, R., Otero, I., Neely, R., Futral, S., Dube, E., McCallen, R., Maltby, J., & and Nichols, A., ALE hydrocode development, Joint DOD/DOE Munitions Technology Development Progress Report, UCRL-ID-103482-95, January 1996.

[9] Dube, E. & Rodrigue, G., A geometric weighted elliptic grid regeneration method for 3D unstructured ALE hydrodynamics, Proc. of the 5th International Symposium on Computational Fluid Dynamics, Sendai, Japan, August 31-September 3, 1993.



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