[en] This report documents the results for the FY07 ASC Integrated Codes Level 2 Milestone number 2354. The description for this milestone is, 'Demonstrate level set free surface tracking capabilities in ARIA to simulate the dynamics of the formation and time evolution of a weld pool in laser welding applications for neutron generator production'. The specialized boundary conditions and material properties for the laser welding application were implemented and verified by comparison with existing, two-dimensional applications. Analyses of stationary spot welds and traveling line welds were performed and the accuracy of the three-dimensional (3D) level set algorithm is assessed by comparison with 3D moving mesh calculations

[en] A truncation error analysis is performed for models based on the lattice Boltzmann (LB) equation. This analysis involves two steps: the recursive application of the LB equation and a Taylor series expansion. Unlike previous analytical studies of LB methods, the present work does not assume an asymptotic relationship between the temporal and spatial discretization parameters or between the probability distribution function, f, and its equilibrium distribution, f^eq. Effective finite difference stencils are derived for both the distribution function and the primitive variables, i.e., density and velocity. The governing partial differential equations are also recovered. The associated truncation errors are derived and the results are validated by numerical simulation of analytic flows. Analysis of the truncation errors elucidates the roles of the kinetic theory relaxation parameter, τ, and the discretization parameters, Δx and Δt. The effects of initial and boundary conditions are also addressed and are shown to significantly affect the overall accuracy of the method

[en] Highlights: • Extension of the Conformal Decomposition Finite Element Method (CDFEM) to multi-material interface interactions. • Solution verification showing ideal order-of-convergence for geometric and physical quantities of interest. • Application of CDFEM to experimental lithium-ion battery electrode mesostructures. • Assessment of representative volume element (RVE) domain sizes and sample-to-sample variability. As computing power rapidly increases, quickly creating a representative and accurate discretization of complex geometries arises as a major hurdle towards achieving a next generation simulation capability. Component definitions may be in the form of solid (CAD) models or derived from 3D computed tomography (CT) data, and creating a surface-conformal discretization may be required to resolve complex interfacial physics. The Conformal Decomposition Finite Element Methods (CDFEM) has been shown to be an efficient algorithm for creating conformal tetrahedral discretizations of these implicit geometries without manual mesh generation. In this work we describe an extension to CDFEM to accurately resolve the intersections of many materials within a simulation domain. This capability is demonstrated on both an analytical geometry and an image-based CT mesostructure representation consisting of hundreds of individual particles. Effective geometric and transport properties are the calculated quantities of interest. Solution verification is performed, showing CDFEM to be optimally convergent in nearly all cases. Representative volume element (RVE) size is also explored and per-sample variability quantified. Relatively large domains and small elements are required to reduce uncertainty, with recommended meshes of nearly 10 million elements still containing upwards of 30% uncertainty in certain effective properties. This work instills confidence in the applicability of CDFEM to provide insight into the behaviors of complex composite materials and provides recommendations on domain and mesh requirements.