Gabi Luttwak

Long rod penetration in oblique impact

The oblique impact and penetration of long rods is investigated both experimentally and numerically. In the experiments a long copper rod impacted obliquely an aluminum plate at a velocity of 850 m/sec. We have chosen ductile materials like aluminum and copper to ensure that the results are not sensitive to the failure model used in the calculations. The low density of the aluminum, and the relatively small sizes of the target plates enabled us to resolve the material interfaces in the X-ray shadowgraph taken during the penetration. The numerical simulations were carried out in the multimaterial Euler-with-strength processor of the three dimensional code MSC/DYTRAN. There is a good agreement between the computations and the experimental results, as to the shape of the projectile and target during the penetration process.

Applying the SMG Scheme to Reactive Flow

The staggered mesh Godunov-SMG scheme for Lagrangian and Arbitrary Lagrangian Eulerian (ALE) hydrodynamics has several potential advantages for applications involving reactive flow simulations arising in the initiation and propagation of detonation. This includes the capabilities to capture discontinuities present in an expanding flow and its inherent hourglass damping property. In the current work, we add to the stagered mesh Godunov (SMG) scheme an appropriate reaction rate law and an equation of state for mixtures of reactants and reaction products, and we test the performance of the scheme to simulate the detonation initiation and propagation over an initially deformed mesh.

Staggered Mesh Godunov (SMG) Schemes for Lagrangian Hydrodynamics

The difficulties inherent in converting the zone‐centered Godunov method into a 3D Lagrangian/ALE scheme have led us to propose an SMG scheme. The SMG/Q version presented here solves internal energy and momentum equations by using only zone‐centered “collision” Riemann problems. It is formulated in a dual Godunov/Classical‐Lagrange way. A limited‐slope approximation of zone‐centered velocity gradients produces a second‐order extension of this method. Basic test cases, both 1D and 3D, demonstrate the SMG/Q features.

Comparing Lagrangian Godunov and Pseudo‐Viscosity Schemes for Multi‐Dimensional Impact Simulations

Modern Eulerian codes use second order Godunov schemes, while Lagrangian calculations are routinely carried out with first order pseudo‐viscosity codes. We compare these, looking for the right scheme to be used in a 3D ALE code, which should handle both Eulerian and Lagrangian meshes. In a Lagrangian Godunov scheme, the grid velocity has to be defined. We first look at schemes based on interpolating the velocities to the vertices, next we consider the advantages of a new staggered mesh Godunov (SGM) scheme. These schemes are tested both with the 1D Sod shock tube problem and the 3D normal impact of square rods into a wall.

Second order discrete rezoning

The efficient solution of many fluid dynamic problems depends on the capability to change the computational mesh during the calculations. Discrete rezoning is customarily used in Lagrangian calculations to prevent grid distortions. We consider a second order accurate, discrete rezoning of multimaterial Euler and ALE calculations. While remapping zones containing more than one single fluid, special attention must to given to properly resolve the material boundaries cutting through the mesh. In a second order scheme, a piecewisely linear density distribution is assumed. We specifically consider here the case of a two dimensional structural grid, but it is straightforward to apply this method to a general connectivity mesh in either two or three dimensions.

Three dimensional numerical simulations of the effect of cyclic perturbations on liner acceleration

We investigate in numerical simulations the effect of cyclic angular disturbances on the liner motion and deformation. The calculations were carried out in the three-dimensional codes MSC/Dytran and Autodyn-3D. Inert inserts inside the charge caused the disturbances. The results show the dependence of the amplitude of the perturbation on the distance of the inserts from the liner. We have also considered the case of cyclic variations in the casing width. We discuss the symmetry of the problem and the numerical techniques utilized in the simulations.

Interface Tracking in Eulerian and MMALE Calculations

In multi‐material Eulerian and MMALE (Multi‐material Arbitrary Lagrangian Eulerian) calculations, the material boundaries may cut through the grid lines and it is necessary to locate their position. Typical Eulerian codes use a Cartesian mesh, but for a MMALE code, the mesh is moving and cannot remain Cartesian. We use a Youngs type 3D interface reconstruction, based on the volumes of the fluid in the neighboring zones. This method was first implemented in the 2D code MMALE. We have since applied it to 3D Cartesian mesh in the code AUTODYN‐3D. In the present work, we show how this approach can be extended to handle a 3D non‐Cartesian MMALE mesh. The advantages and the limitations of the method are discussed, and we consider ways to further improve it.

Numerical simulations of rod-plate interaction

The 30° oblique impact between a high speed copper rod and a moving steel plate is investigated. The numerical simulations are carried out in the second order, multi-material Euler-Godunov processor of Autodyn V4. The full three dimensional calculation is compared to an approximate, two dimensional plane strain simulations. The results are compared to available experimental data. The three dimensional effects are considered and the validity of using the 2D approximation is discussed.

Virtual memory techniques in Eulerian calculations

In an Eulerian formulation, the mesh has to span the space which may be reached by the materials during the calculation. Thus, many more zones are required, than for a similar Lagrangian, body-fitted grid. For typical 3D problems, to achieve an acceptable resolution using traditional Eulerian schemes, the memory requirements may exceed the available resources. We present a virtual memory technique implemented in the Autodyn 3D second order Godunov solver. Using this innovative approach, the empty cells in the mesh need only to store the cell geometry. Only non-empty zones are processed, resulting in substantial gains in both the computational memory, as well as in the speed of the computation. The efficiency and accuracy of the Eulerian virtual memory approach is illustrated by the simulation of the 45° oblique impact of a copper rod, moving at 850 m/sec, into an aluminum target and the comparison of the results with published experimental data(1).

NUMERICAL SIMULATION OF WATER JET PENETRATION

We present a new method for the full numerical simulation of the penetration of a high speed jet. This approach will be especially well suited for the case of the perforation of a multilayered medium by a hypervelocity water jet. We work in convected coordinates. The calculation in the target is almost Langrangian, in the sense that the material boundaries are kept as grid lines. The jet is simulated in an almost Eulerian way, and the water is allowed to flow through the mesh. The results for the impact of a water jet moving with a speed of 3 mm/μsec on a bilayered target made of aluminium and plexiglass are presented.