Samuel R. Subia

Aria 1.5 : user manual.

Aria is a Galerkin finite element based program for solving coupled-physics problems described by systems of PDEs and is capable of solving nonlinear, implicit, transient and direct-to-steady state problems in two and three dimensions on parallel architectures. The suite of physics currently supported by Aria includes the incompressible Navier-Stokes equations, energy transport equation, species transport equations, nonlinear elastic solid mechanics, and electrostatics as well as generalized scalar, vector and tensor transport equations. Additionally, Aria includes support for arbitrary Lagrangian-Eulerian (ALE) and level set based free and moving boundary tracking. Coupled physics problems are solved in several ways including fully-coupled Newtons method with analytic or numerical sensitivities, fully-coupled Newton-Krylov methods, fully-coupled Picards method, and a loosely-coupled nonlinear iteration about subsets of the system that are solved using combinations of the aforementioned methods. Error estimation, uniform and dynamic h-adaptivity and dynamic load balancing are some of Arias more advanced capabilities. Aria is based on the Sierra Framework.

Computational thermal, chemical, fluid, and solid mechanics for geosystems management.

This document summarizes research performed under the SNL LDRD entitled - Computational Mechanics for Geosystems Management to Support the Energy and Natural Resources Mission. The main accomplishment was development of a foundational SNL capability for computational thermal, chemical, fluid, and solid mechanics analysis of geosystems. The code was developed within the SNL Sierra software system. This report summarizes the capabilities of the simulation code and the supporting research and development conducted under this LDRD. The main goal of this project was the development of a foundational capability for coupled thermal, hydrological, mechanical, chemical (THMC) simulation of heterogeneous geosystems utilizing massively parallel processing. To solve these complex issues, this project integrated research in numerical mathematics and algorithms for chemically reactive multiphase systems with computer science research in adaptive coupled solution control and framework architecture. This report summarizes and demonstrates the capabilities that were developed together with the supporting research underlying the models. Key accomplishments are: (1) General capability for modeling nonisothermal, multiphase, multicomponent flow in heterogeneous porous geologic materials; (2) General capability to model multiphase reactive transport of species in heterogeneous porous media; (3) Constitutive models for describing real, general geomaterials under multiphase conditions utilizing laboratory data; (4) General capability to couple nonisothermal reactive flow with geomechanics (THMC); (5) Phase behavior thermodynamics for the CO2-H2O-NaCl system. General implementation enables modeling of other fluid mixtures. Adaptive look-up tables enable thermodynamic capability to other simulators; (6) Capability for statistical modeling of heterogeneity in geologic materials; and (7) Simulator utilizes unstructured grids on parallel processing computers.

Solution-verified reliability analysis and design of bistable MEMS using error estimation and adaptivity.

This report documents the results for an FY06 ASC Algorithms Level 2 milestone combining error estimation and adaptivity, uncertainty quantification, and probabilistic design capabilities applied to the analysis and design of bistable MEMS. Through the use of error estimation and adaptive mesh refinement, solution verification can be performed in an automated and parameter-adaptive manner. The resulting uncertainty analysis and probabilistic design studies are shown to be more accurate, efficient, reliable, and convenient.

Ray tracing in a finite-element domain using nodal basis functions.

A method is presented for tracing rays through a medium discretized as finite-element volumes. The ray-trajectory equations are cast into the local element coordinate frame, and the full finite-element interpolation is used to determine instantaneous index gradient for the ray-path integral equation. The finite-element methodology is also used to interpolate local surface deformations and the surface normal vector for computing the refraction angle when launching rays into the volume, and again when rays exit the medium. The procedure is applied to a finite-element model of an optic with a severe refractive-index gradient, and the results are compared to the closed-form gradient ray-path integral approach.

A Methodology for Modelling Enclosure Radiation Heat Transfer Under Large Structural Deformation

Finite element method (FEM) numerical simulations of heat transfer for high-temperature regimes often require modeling of grey-body enclosure radiation where enclosure geometry definitions are obtained as part of the model grid generation process. Owing to the expense of solving the radiation problem, typical FEM approaches loosely couple the radiative transfer solution as boundary conditions to a standard conduction formulation. When the problem at hand is thermal-mechanical and relative motion occurs between enclosure surfaces, the simulation code is tasked with providing a means of updating the original enclosure surface geometry to reflect the deformed configuration. While this scenario is manageable for contiguously meshed discretizations, the difficulty of updating enclosure geometry is greatly increased when the model admits sliding. Here the analysis code must employ both mechanical and thermal contact, relying heavily on geometric search and contact constraints to enforce closure for the conduction formulation.General purpose large-deformation FEM structural codes employ surface contact utilities to provide geometric search and contact constraint definitions. This paper describes an ongoing effort to leverage contact utilities for solving the enclosure radiation problem in deforming and sliding mesh scenarios while having minimal impact to a traditional modeling approach. The current effort is divided into two areas, enclosure definitions and thermal contact, but the primary focus here is on enabling use of contact to provide definition of the enclosure. The proposed methodology is demonstrated on simple enclosure radiation models using SNL Sierra Mechanics Dash contact utilities and the Chaparral enclosure radiation library with Sierra Mechanics Structural and Thermal application codes.Sandia National Laboratories is a multi-program laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the U.S. Department of Energys National Nuclear Security Administration under contract DE-AC04-94AL85000.Copyright