Mark A. Kenamond

An approach for treating contact surfaces in Lagrangian cell-centered hydrodynamics

A new method is presented for modeling contact surfaces in Lagrangian cell-centered hydrodynamics (CCH). The contact method solves a multi-directional Riemann-like problem at each penetrating or touching node along the contact surface. The velocity of a penetrating or touching node and the corresponding forces are explicitly calculated using the Riemann-like nodal solver. The contact method works with material strength and allows surfaces to impact, slide, and separate. Results are presented for several test problems involving both gases and materials with strength. The new contact surface approach extends the modeling capabilities of CCH.

Reduction of dissipation in Lagrange cell-centered hydrodynamics (CCH) through corner gradient reconstruction (CGR)

This work presents an extension of a second order cell-centered hydrodynamics scheme on unstructured polyhedral cells 13 toward higher order. The goal is to reduce dissipation, especially for smooth flows. This is accomplished by multiple piecewise linear reconstructions of conserved quantities within the cell. The reconstruction is based upon gradients that are calculated at the nodes, a procedure that avoids the least-square solution of a large equation set for polynomial coefficients. Conservation and monotonicity are guaranteed by adjusting the gradients within each cell corner. Results are presented for a wide variety of test problems involving smooth and shock-dominated flows, fluids and solids, 2D and 3D configurations, as well as Lagrange, Eulerian, and ALE methods.

Estimation of Metal Strength at Very High Rates Using Free-Surface Richtmyer–Meshkov Instabilities

Recently, Richtmyer–Meshkov Instabilities (RMI) have been proposed for studying the average strength at strain rates up to at least 107/s. RMI experiments involve shocking a metal interface that has initial sinusoidal perturbations. The perturbations invert and grow subsequent to shock and may arrest because of strength effects. In this work we present new RMI experiments and data on a copper target that had five regions with different perturbation amplitudes on the free surface opposite the shock. We estimate the high-rate, low-pressure copper strength by comparing experimental data with Lagrangian numerical simulations. From a detailed computational study we find that mesh convergence must be carefully addressed to accurately compare with experiments, and numerical viscosity has a strong influence on convergence. We also find that modeling the as-built perturbation geometry rather than the nominal makes a significant difference. Because of the confounding effect of tensile damage on total spike growth, which has previously been used as the metric for estimating strength, we instead use a new strength metric: the peak velocity during spike growth. This new metric also allows us to analyze a broader set of experimental results that are sensitive to strength because some larger initial perturbations grow unstably to failure and so do not have a finite total spike growth.

Compatible, energy conserving, bounds preserving remap of hydrodynamic fields for an extended ALE scheme

Abstract From the very origins of numerical hydrodynamics in the Lagrangian work of von Neumann and Richtmyer [83] , the issue of total energy conservation as well as entropy production has been problematic. Because of well known problems with mesh deformation, Lagrangian schemes have evolved into Arbitrary Lagrangian–Eulerian (ALE) methods [39] that combine the best properties of Lagrangian and Eulerian methods. Energy issues have persisted for this class of methods. We believe that fundamental issues of energy conservation and entropy production in ALE require further examination. The context of the paper is an ALE scheme that is extended in the sense that it permits cyclic or periodic remap of data between grids of the same or differing connectivity. The principal design goals for a remap method then consist of total energy conservation, bounded internal energy, and compatibility of kinetic energy and momentum. We also have secondary objectives of limiting velocity and stress in a non-directional manner, keeping primitive variables monotone, and providing a higher than second order reconstruction of remapped variables. In particular, the new contributions fall into three categories associated with: energy conservation and entropy production, reconstruction and bounds preservation of scalar and tensor fields, and conservative remap of nonlinear fields. The paper presents a derivation of the methods, details of implementation, and numerical results for a number of test problems. The methods requires volume integration of polynomial functions in polytopal cells with planar facets, and the requisite expressions are derived for arbitrary order.