Brian Carnes

Final Report on LDRD Project: Coupling Strategies for Multi-Physics Applications

Many current and future modeling applications at Sandia including ASC milestones will critically depend on the simultaneous solution of vastly different physical phenomena. Issues due to code coupling are often not addressed, understood, or even recognized. The objectives of the LDRD has been both in theory and in code development. We will show that we have provided a fundamental analysis of coupling, i.e., when strong coupling vs. a successive substitution strategy is needed. We have enabled the implementation of tighter coupling strategies through additions to the NOX and Sierra code suites to make coupling strategies available now. We have leveraged existing functionality to do this. Specifically, we have built into NOX the capability to handle fully coupled simulations from multiple codes, and we have also built into NOX the capability to handle Jacobi Free Newton Krylov simulations that link multiple applications. We show how this capability may be accessed from within the Sierra Framework as well as from outside of Sierra. The critical impact from this LDRD is that we have shown how and have delivered strategies for enabling strong Newton-based coupling while respecting the modularity of existing codes. This will facilitate the use of these codes in a coupled manner to solve multi-physic applications.

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 Compliant Micro-Electro-Mechanical Systems

An important component of verification and validation of computational models is solution verification, which focuses on the convergence of the desired solution quantities as one refines the spatial and temporal discretizations and iterative controls. Uncertainty analyses often treat solution verification as a separate issue, hopefully through the use of a priori grid convergence studies and selection of models with acceptable discretization errors. In this paper, a tighter connection between solution verification and uncertainty quantification is investigated. In particular, error estimation techniques, using global norm and quantity of interest error estimators, are applied to the nonlinear structural analysis of microelectromechanical systems (MEMS). Two primary approaches for uncertainty quantification are then developed: an error-corrected approach, in which simulation results are directly corrected for discretization errors, and an error-controlled approach, in which estimators are used to drive adaptive h-refinement of mesh discretizations. The former requires quantity of interest error estimates that are quantitatively accurate, whereas the latter can employ any estimator that is qualitatively accurate. Combinations of these error-corrected and error-controlled approaches are also explored. Each of these techniques treats solution verification and uncertainty analysis as a coupled problem, recognizing that the simulation errors may be influenced by, for example, conditions present in the tails of input probability distributions. The most effective and affordable of these approaches are carried forward in probabilistic design studies for robust and reliable operation of a bistable MEMS device. Computational results show that on-line and parameter-adaptive solution verification can lead to uncertainty quantification and design under uncertainty studies that are more accurate, efficient, reliable, and convenient.

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.

Thermal contact algorithms in SIERRA mechanics : mathematical background, numerical verification, and evaluation of performance.

We examine algorithms for the finite element approximation of thermal contact models. We focus on the implementation of thermal contact algorithms in SIERRA Mechanics. Following the mathematical formulation of models for tied contact and resistance contact, we present three numerical algorithms: (1) the multi-point constraint (MPC) algorithm, (2) a resistance algorithm, and (3) a new generalized algorithm. We compare and contrast both the correctness and performance of the algorithms in three test problems. We tabulate the convergence rates of global norms of the temperature solution on sequentially refined meshes. We present the results of a parameter study of the effect of contact search tolerances. We outline best practices in using the software for predictive simulations, and suggest future improvements to the implementation.