Christopher Joseph Garasi

Pulsed-power-driven high energy density physics and inertial confinement fusion research

The Z accelerator [R. B. Spielman, W. A. Stygar, J. F. Seamen et al., Proceedings of the 11th International Pulsed Power Conference, Baltimore, MD, 1997, edited by G. Cooperstein and I. Vitkovitsky (IEEE, Piscataway, NJ, 1997), Vol. 1, p. 709] at Sandia National Laboratories delivers ∼20MA load currents to create high magnetic fields (>1000T) and high pressures (megabar to gigabar). In a z-pinch configuration, the magnetic pressure (the Lorentz force) supersonically implodes a plasma created from a cylindrical wire array, which at stagnation typically generates a plasma with energy densities of about 10MJ∕cm3 and temperatures >1keV at 0.1% of solid density. These plasmas produce x-ray energies approaching 2MJ at powers >200TW for inertial confinement fusion (ICF) and high energy density physics (HEDP) experiments. In an alternative configuration, the large magnetic pressure directly drives isentropic compression experiments to pressures >3Mbar and accelerates flyer plates to >30km∕s for equation of state ...

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

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

\nabla \times \nabla \times

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

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.

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

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.

Three-dimensional z-pinch wire array modeling with ALEGRA-HEDP.

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.

Measurement and modeling of the implosion of wire arrays with seeded instabilities

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

ALEGRA : version 4.6.

\nabla \times \nabla \>{\times}

ALEGRA: User Input and Physics Descriptions Version 4.2

operator on coarse grids. While these null-space properties are critical, they are not enough to guarantee

Case study: Visual debugging of finite element codes

h