Allen C. Robinson

An Improved Algebraic Multigrid Method for Solving Maxwell's Equations

We propose two improvements to the Reitzinger and Schoberl algebraic multigrid (AMG) method for solving the eddy current approximations to Maxwells equations. The main focus in the Reitzinger/Schoberl method is to maintain null space properties of the weak

Mass and penetration depth of Shoemaker‐Levy 9 fragments from time‐resolved photometry

\nabla \times \nabla \times

ALEGRA : an arbitrary Lagrangian-Eulerian multimaterial, multiphysics code.

operator on coarse grids. While these null space properties are critical, they are not enough to guarantee h-independent convergence of the overall multigrid method. We illustrate how the Reitzinger/Schoberl AMG method loses h-independence due to the somewhat limited approximation property of the grid transfer operators. We present two improvements to these operators that not only maintain the important null space properties on coarse grids but also yield significantly improved multigrid convergence rates. The first improvement is based on smoothing the Reitzinger/Schoberl grid transfer operators. The second improvement is obtained by using higher order nodal interpolation to derive the corresponding AMG interpolation operators. While not completely h-independent, the resulting AMG/CG method demonstrates improved convergence behavior while maintaining low operator complexity.

Self-consistent, two-dimensional, magnetohydrodynamic simulations of magnetically driven flyer plates

Computational simulations of the first 100 seconds of interaction of Shoemaker-Levy 9 fragments with the Jovian atmosphere have revealed a potential method for estimating the masses and penetration depths of the individual objects. For sufficiently large fragments, impact-generated fireballs will rise into line-of-sight over the Jovian limb (less than one minute after impact for a 3-km diameter fragment). It is possible that time-resolved radiometric measurements from Earth- and orbital-based observatories may detect two different arrivals for each impact: first the shock wave and, a few seconds later, a debris front (fireball). Measurements of one or both arrival times with time resolutions of better than one second will provide information that would place strong restrictions on the range of values of equivalent explosive yield (from which fragment mass can be extracted) and effective penetration depth. We believe that time-resolved photometry measurements of impact-induced light emission (impact-flash signatures) will provide the best means by which Shoemaker-Levy 9 fragment masses can be determined if they are greater than about 5×1015 g (corresponding to a 1-km diameter ice sphere).

Multi-dimensional high energy density physics modeling and simulation of wire array Z-pinch physics

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.

The impact of comet Shoemaker-Levy 9 on Jupiter

The intense magnetic field generated by the 20 megaampere Z machine [R. B. Spielman et al., Phys. Plasmas 5, 2105 (1998)] at Sandia National Laboratories is being used as a pressure source for material science studies. An application we have studied in great detail involves using the intense magnetic field to accelerate flyer plates (small metal disks) to very high velocities (>20 km/s) for use in shock loading experiments. We have used two-dimensional (2D) magnetohydrodynamic (MHD) simulation to investigate the physics of accelerating flyer plates using multi-megabar magnetic drive pressures. A typical shock physics load is comprised of conducting electrodes that are highly compressible at multi-megabar pressures. Electrode deformation that occurs during the rise time of the current pulse causes significant inductance increase, which reduces the peak current (drive pressure) relative to a static geometry. This important dynamic effect is modeled self-consistently by driving the MHD simulation with an acc...

The impact of periodic comet shoemaker-levy 9 on jupiter

The two- and three-dimensional (2D and 3D) versions of ALEGRA-HEDP [A. C. Robinson and C. J. Garasi, “Three-dimensional Z-pinch wire array modeling,” Computer Physics Communications, submitted] have been utilized to simulate discrete wire effects including precursor formation in 2D (r-θ plane) and nonuniform axial ablation (3D). Comparisons made between 2D and 3D simulations indicate that 2D simulations overestimate the mass ablation rate by a factor of 10–100 with respect to the 3D case, causing pre-mature motion of the array with respect to experimental data. Additionally, the 2D case advects a factor of 5 more current to axis than the 3D case. The integrity of the simulations is assessed by comparing the results to laser imaging of wire ablation and array trajectory information inferred from visible and x-ray imaging. Comparisons to previously proposed ablation models are also presented. These simulations represent the first high-fidelity three-dimensional calculations of wire-array pinch geometries.

Toward an h-Independent Algebraic Multigrid Method for Maxwell's Equations

We have performed computational shock-physics simulations of the hypervelocity (60 km/s) impact of 1–3 km, water-ice spheres entering a hydrogen-helium Jovian atmosphere. These conditions simulate the best current estimates for the collision of fragments of periodic comet Shoemaker-Levy 9 with Jupiter in July, 1994. We used the Eulerian shock-physics code CTH, and its parallel version PCTH to perform 2-D analyses of penetration and breakup, and 3-D analyses of the growth of the resulting fireball during the first 100 seconds after fragment entry. We can use our simulations to make specific predictions of the time interval between fragment entry and fireball arrival into line-of-sight from the earth. For a fragment larger than about 1 km, we believe that the time of fireball arrival above Jupiters limb will be directly observable from earth. Measurements of this time by observers, in conjunction with our simulations, may allow mass of cometary fragments to be determined.

Acceleration instability in elastic‐plastic solids. I. Numerical simulations of plate acceleration

Abstract We have performed computational shock-physics simulations of the hypervelocity (60 km/s) impact of l-3 km, water-ice spheres entering a hydrogen-helium Jovian atmosphere, conditions that simulate current estimates for the collision of fragments of Periodic Comet Shoemaker-Levy 9 with Jupiter. Observatories in space and around the world observed the events as they occurred in July, 1994. The Hubble Space Telescope obtained high resolution images of the impact-generated fireballs that appeared above the limb of Jupiter and of the visibly dark ejecta patterns distributed over broad regions of the Jovian stratosphere. Time-resolved radiometric measurements from spacecraft and Earth-based observatories detected multiple arrivals for each impact: the entry flash as the incoming, fragment entered the atmosphere, arrival of the debris front (fireball) as it emerged above the Jovian limb (which varies as a function of wavelength), the arrival of the debris front into sunlight and finally, the emergence of the impact site as it rotated into view. We used the Eulerian shock-physics code CTH, and its parallel version PCTH to perform 2-E) analyses of penetration and breakup, and 3-D analyses of the growth of the resulting fireball during the first 120 seconds after fragment entry. For sufficiently large fragments, impact-generated fireballs rise into line-of-sight over the Jovian limb. For land 3-km fragments impacting 6 beyond the limb, this occurs approximately 75 and 50 seconds after impact, respectively. Measurement of the time interval between fragment entry and limb arrival provides information that places strong restrictions on equivalent explosive yield (from which fragment mass can be estimated). Measurements of more arrivals help constrain the effective penetration depth, thereby lending insight into the material and mechanical properties of the cometary fragments. We believe that matching high resolution imagery and time-resolved photometry with numerical simulations will provide some of the best means by which Shoemaker-Levy 9 fragment masses and material properties will be determined.

Acceleration instability in elastic‐plastic solids. II. Analytical techniques

We propose a new algebraic multigrid (AMG) method for solving the eddy current approximations to Maxwells equations. This AMG method has its roots in an algorithm proposed by Reitzinger and Schoberl. The main focus in the Reitzinger and Schoberl method is to maintain null-space properties of the weak