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. (c) 2017 Elsevier Inc. All rights reserved.

The computational efficiency of existing hydrocodes is expected to suffer as computer architectures advance beyond the traditional parallel central processing unit (CPU) model . Concerning new computer architectures, sources of relative performance degradation might include reduced memory bandwidth per core, increased resource contention due to concurrency, increased single instruction, multiple data (SIMD) length, and increasingly complex memory hierarchies. Concerning existing codes, any performance degradation will be influenced by a lack of attention to performance in their design and implementation.This work reports on considerations for improving computational performance in preparation for current and expected changes to computer architecture. The algorithms studied will include increasingly complex prototypes for radiation hydrodynamics codes, such as gradient routines and diffusion matrix assembly (e.g., in [1-6]). The meshes considered for the algorithms are structured or unstructured meshes. The considerations applied for performance improvements are meant to be general in terms of architecture (not specifically graphical processing unit (GPUs) or multi-core machines, for example) and include techniques for vectorization, threading, tiling, and cache blocking. Out of a survey of optimization techniques on applications such as diffusion and hydrodynamics, we make general recommendations with a view toward making these techniques conceptually accessible to the applications code developer. Published 2015. This article is a U.S. Government work and is in the public domain in the USA.

We present the ongoing development and implementation of an ejecta model in the FLAG hydrocode. Ejecta is the term given to particulate matter that is produced at the free surface of a material subject to extreme shock loading. Following shock propagation into a material and reflection at its free surface, conditions may be sufficient to induce phase changes, damage, or fragmentation at the surface. The dynamics of the fragmentation may be such that a “cloud” of particulate matter forms and propagates away from the material.Modeling such phenomena in a continuum hydrodynamics code challenges the assumptions underlying the numerical approximations made in the hydrodynamics. The representative scales for the particulate matter are often much smaller than the representative scales for the bulk material producing the ejecta. However, this scale separation allows for statistical descriptions of ejecta that are compatible with continuum mechanics.Earlier work documents an initial effort in modeling ejecta in the FLAG hydrocode. The FLAG hydrocode computes continuum mechanics solutions for fluid and solid materials in an Arbitrary–Eulerian–Lagrangian (ALE) framework. To model ejecta in FLAG, a hybrid particle-continuum representation was defined that allows for coupling with continuum materials on large (bulk) scales. Numerical models were developed and implemented for particle production (sourcing) as well as for solving the particle equations of motion. The numerics were shown to conserve mass, momentum and energy, and preliminary results were given for modeling drag and volume effects.This work documents recent advances in source and transport models. Spatial and temporal dependencies have been added to the source models to account for geometric free-surface variations, mesh dependence, and shock loading. More physically relevant drag models have been implemented that include Reynolds number effects. These will be presented along with test results verifying the models. A FLAG model of an actual ejecta experiment will also be presented.

We did not run with a 'cylindrically painted region'. However, we did compute two general variants of the original problem. Refinement studies where a single zone at each level of refinement contains the entire internal energy at t=0 or A 'finite' energy source which has the same physical dimensions as that for the 91 x 46 mesh, but consisting of increasing numbers of zones with refinement. Nominal mesh resolution: 91 x 46. Other mesh resolutions: 181 x 92 and 361 x 184. Note, not identical to the original specification. To maintain symmetry for the 'fixed' energy source, the mesh resolution was adjusted slightly. FLAG Lagrange or full (Eulerian) ALE was used with various options for each simulation. Observation - for either Lagrange or ALE, point or 'fixed' source, calculations converge on density and pressure with mesh resolution, but not energy, (not vorticity either).

Lagrangian hydrodynamics of strength‐free materials continues to present open issues, even in one dimension. We focus on the problem of closing a system of equations for a two‐material cell under the assumption of a single velocity model. There are several existing models and approaches, each possessing different levels of fidelity to the underlying physics and each exhibiting unique features in the computed solutions. We consider three models that take different approaches to breaking the assumption of instantaneous pressure equilibration in the mixed‐material cell. The first of these is the well‐known method of Tipton, in which a viscosity‐like pressure relaxation term is coupled with an otherwise isentropic pressure update to obtain closed‐form expressions for the materials' volume fractions and corresponding sub‐cell pressures. The second is the physics‐inspired, geometry‐based pressure relaxation model of Kamm and Shashkov, which is based on an optimization procedure that uses a local, exact Riemann problem. The third model is the unique aspect of this paper, inspired by the work of Delov and Sadchikov and Goncharov and Yanilkin. This sub‐scale dynamics approach is motivated by the linearized Riemann problem to initialize volume fraction changes, which are then modified, via the materials' SIEs, to drive the mixed cell toward pressure equilibrium. Each of these approaches is packaged in the framework of a two‐step time integration scheme. We compare these multi‐material pressure relaxation models, together with corresponding pure‐material calculations, on idealized, two‐material problems with either ideal‐gas or stiffened‐gas equations of state. Published in 2010 by John Wiley & Sons, Ltd.

We have extended the Sub-Scale Dynamics (SSD) closure model for multi-fluid computational cells. Volume exchange between two materials is based on the interface area and a notional interface translation velocity, which is derived from a linearized Riemann solution. We have extended the model to cells with any number of materials, computing pressure-difference-driven volume and energy exchange as the algebraic sum of pairwise interactions. In multiple dimensions, we rely on interface reconstruction to provide interface areas and orientations, and centroids of material polygons. In order to prevent unphysically large or unmanageably small material volumes, we have used a flux-corrected transport (FCT) approach to limit the pressure-driven part of the volume exchange. We describe the implementation of this model in two dimensions in the FLAG hydrodynamics code. We also report on Lagrangian test calculations, comparing them with others made using a mixed-zone closure model due to Tipton, and with corresponding calculations made with only single-material cells. We find that in some cases, the SSD model more accurately predicts the state of material in mixed cells. By comparing the algebraic forms of both models, we identify similar dependencies on state and dynamical variables, and propose explanations for the apparent higher fidelity of the SSD model.

We discuss the high fidelity simulation, the identification of dominant scales, the design of a computational superstructure for time integration of the dominant-scale dynamics, and associated results. The results include accurate short and medium-time tracking of the dominant-scale dynamics for a range of parameter values for the computational superstructure. These results suggest that coarse analysis methods are useful for solving fluid flow problems of a multiscale nature.

Recent studies of the micro-dynamic behavior of a deployable telescope metering truss have identified instabilities in the equilibrium shape of the truss in response to low-energy dynamic loading. Analyses indicate that these micro-dynamic instabilities arise from stick-slip friction within the truss joints (e.g., hinges and latches). The present study characterizes the low-magnitude quasi-static load-cycle response of the precision revolute joints incorporated in the deployable telescope metering truss, and specifically, the hysteretic response of these joints caused by stick-slip friction within the joint. Detailed descriptions are presented of the test setup and data reduction algorithms, including discussions of data-error sources and data-filtering techniques. Test results are presented from thirteen specimens, and the effects of joint preload and manufacturing tolerances are investigated. Using a simplified model of stick-slip friction, a relationship is made between joint load-cycle behavior and micro-dynamic dimensional instabilities in the deployable telescope metering truss.

This paper describes the development of transfer function models for the trailing edge and upper- and lower-spoiler actuators of the Benchmark Active Control Technology (BACT) wind-tunnel model for application to control system analysis and design. A simple nonlinear least squares parameter estimation approach is applied to determine transfer function parameters from frequency response data. Unconstrained quasi-Newton minimization of weighted frequency response error was employed to estimate the transfer function parameters. An analysis of the behavior of the actuators over time to assess the effects of wear and aerodynamic load using the transfer function models is also presented. The frequency responses indicate consistent actuator behavior throughout the wind-tunnel test and only slight degradation in effectiveness due to aerodynamic hinge loading. The resulting actuator models have been used in design, analysis, and simulation of controllers for the BACT. The resulting controllers have successfully suppressed flutter over a wide range of conditions.