Thomas Eugene Voth

Characteristics of semi- and full discretization of stabilized Galerkin meshfree method

Stabilized conforming nodal integration (SCNI) has been developed to enhance computational efficiency of Galerkin meshfree methods. This paper employs von Neumann analyses to study the spatial semi-discretization of Galerkin meshfree methods using SCNI. Two model problems were presented with respect to the normalized phase speed and group speed for the wave equation, and normalized diffusivity for the heat equation. Both consistent and lumped mass (capacity) discretizations are considered in the study. The transient properties in the full discretization of the two model problems were also analyzed. The results show superior dispersion behavior in meshfree methods integrated by SCNI compared to the Gauss integration when consistent mass (capacity) matrix is employed in the discretization. For the lumped mass case, SCNI performance is comparable to that of the Gauss integration, but exhibits considerable reduction of computational time.

ACME: Algorithms for Contact in a Multiphysics Environment API Version 1.3

An effort is underway at Sandia National Laboratories to develop a library of algorithms to search for potential interactions between surfaces represented by analytic and discretized topological entities. This effort is also developing algorithms to determine forces due to these interactions for transient dynamics applications. This document describes the Application Programming Interface (API) for the ACME (Algorithms for Contact in a Multiphysics Environment) library.

Results of von Neumann analyses for reproducing kernel semi-discretizations†

The reproducing kernel particle method (RKPM) has many attractive properties that make it ideal for treating a broad class of physical problems. RKPM may be implemented in a ‘mesh-full’ or a ‘mesh-free’ manner and provides the ability to tune the method, via the selection of a window function and its associated dilation parameter, in order to achieve the requisite numerical performance. RKPM also provides a framework for performing hierarchical computations making it an ideal candidate for simulating multi-scale problems. Although the method has many appealing attributes, it is quite new and its numerical performance is still being quantified with respect to more traditional discretization techniques. In order to assess the numerical performance of RKPM, detailed studies of the method on a series of model partial differential equations has been undertaken. The results of von Neumann analyses for RKPM semi-discretizations of one and two-dimensional, first- and second-order wave equations are presented in the form of phase and group errors. Excellent dispersion characteristics are found for the consistent mass matrix with the proper choice of dilation parameter. In contrast, row-sum lumping the mass matrix is demonstrated to introduce severe lagging phase errors. A ‘higher-order’ mass matrix improves the dispersion characteristics relative to the lumped mass matrix but also yields significant lagging phase errors relative to the fully integrated, consistent mass matrix. Published in 2000 by John Wiley & Sons, Ltd.

Discretization errors associated with reproducing kernel methods: one-dimensional domains ☆

Abstract The reproducing kernel particle method (RKPM) is a discretization technique for partial differential equations that uses the method of weighted residuals, classical reproducing kernel theory and modified kernels to produce either “mesh-free” or “mesh-full” methods. Although RKPM has many appealing attributes, the method is new, and its numerical performance is just beginning to be quantified. In order to address the numerical performance of RKPM, von Neumann analysis is performed for semi-discretizations of three model one-dimensional PDEs. The von Neumann analyses results are used to examine the global and asymptotic behavior of the semi-discretizations. The model PDEs considered for this analysis include the parabolic and hyperbolic (first- and second-order wave) equations. Numerical diffusivity for the former and phase speed for the latter are presented over the range of discrete wavenumbers and in an asymptotic sense as the particle spacing tends to zero. Group speed is also presented for the hyperbolic problems. Excellent diffusive and dispersive characteristics are observed when a consistent mass matrix formulation is used with the proper choice of refinement parameter. In contrast, the row-sum lumped mass matrix formulation severely degraded performance. The asymptotic analysis indicates that very good rates of convergence (O( x 6 )–O( x 8 )) are possible when the consistent mass matrix formulation is used with an appropriate choice of refinement parameter and quadrature rule.

ALEGRA : version 4.6.

ALEGRA is an arbitrary Lagrangian-Eulerian multi-material finite element code used for modeling solid dynamics problems involving large distortion and shock propagation. This document describes the basic user input language and instructions for using the software.

ALEGRA: User Input and Physics Descriptions Version 4.2

ALEGRA is an arbitrary Lagrangian-Eulerian finite element code that emphasizes large distortion and shock propagation. This document describes the user input language for the code.

On the Development of the Large Eddy Simulation Approach for Modeling Turbulent Flow: LDRD Final Report

This report describes research and development of the large eddy simulation (LES) turbulence modeling approach conducted as part of Sandias laboratory directed research and development (LDRD) program. The emphasis of the work described here has been toward developing the capability to perform accurate and computationally affordable LES calculations of engineering problems using unstructured-grid codes, in wall-bounded geometries and for problems with coupled physics. Specific contributions documented here include (1) the implementation and testing of LES models in Sandia codes, including tests of a new conserved scalar--laminar flamelet SGS combustion model that does not assume statistical independence between the mixture fraction and the scalar dissipation rate, (2) the development and testing of statistical analysis and visualization utility software developed for Exodus II unstructured grid LES, and (3) the development and testing of a novel new LES near-wall subgrid model based on the one-dimensional Turbulence (ODT) model.

LDRD final report : mesoscale modeling of dynamic loading of heterogeneous materials.

Material response to dynamic loading is often dominated by microstructure (grain structure, porosity, inclusions, defects). An example critically important to Sandias mission is dynamic strength of polycrystalline metals where heterogeneities lead to localization of deformation and loss of shear strength. Microstructural effects are of broad importance to the scientific community and several institutions within DoD and DOE; however, current models rely on inaccurate assumptions about mechanisms at the sub-continuum or mesoscale. Consequently, there is a critical need for accurate and robust methods for modeling heterogeneous material response at this lower length scale. This report summarizes work performed as part of an LDRD effort (FY11 to FY13; project number 151364) to meet these needs.

AN EXTENDED FINITE ELEMENT METHOD FORMULATION FOR MODELING THE RESPONSE OF POLYCRYSTALLINE MATERIALS TO DYNAMIC LOADING

The eXtended Finite Element Method (X‐FEM) is a finite‐element based discretization technique developed originally to model dynamic crack propagation [1]. Since that time the method has been used for modeling physics ranging from static meso‐scale material failure to dendrite growth. Here we adapt the recent advances of Vitali and Benson [2] and Song et al. [3] to model dynamic loading of a polycrystalline material. We use demonstration problems to examine the methods efficacy for modeling the dynamic response of polycrystalline materials at the meso‐scale. Specifically, we use the X‐FEM to model grain boundaries. This approach allows us to i) eliminate ad‐hoc mixture rules for multi‐material elements and ii) avoid explicitly meshing grain boundaries.

Semi-Infinite Target Penetration by Ogive-Nose Penetrators: ALEGRA/SHISM Code Predictions for Ideal and Non-Ideal Impacts

The physics of ballistic penetration mechanics is of great interest in penetrator and counter-measure design. The phenomenology associated with these events can be quite complex and a significant number of studies have been conducted ranging from purely experimental to ‘engineering’ models based on empirical and/or analytical descriptions to fully-coupled penetrator/target, thermo-mechanical numerical simulations. Until recently, however, there appears to be a paucity of numerical studies considering ‘non-ideal’ impacts [1]. The goal of this work is to demonstrate the SHISM algorithm implemented in the ALEGRA Multi-Material ALE (Arbitrary Lagrangian Eulerian) code [13]. The SHISM algorithm models the three-dimensional continuum solid mechanics response of the target and penetrator in a fully coupled manner. This capability allows for the study of ‘non-ideal’ impacts (e.g. pitch, yaw and/or obliquity of the target/penetrator pair). In this work predictions using the SHISM algorithm are compared to previously published experimental results for selected ideal and non-ideal impacts of metal penetrator-target pairs. These results show good agreement between predicted and measured maximum depth-of-penetration, DOP, for ogive-nose penetrators with striking velocities in the 0.5 to 1.5 km/s range. Ideal impact simulations demonstrate convergence in predicted DOP for the velocity range considered. A theory is advanced to explain disagreement between predicted and measured DOP at higher striking velocities. This theory postulates uncertainties in angle-of-attack for the observed discrepancies. It is noted that material models and associated parameters used here, were unmodified from those in the literature. Hence, no tuning of models was performed to match experimental data.Copyright