Publications

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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.

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In this report, we summarize our work on developing a production level foam processing computational model suitable for predicting the self-expansion of foam in complex geometries. The model is based on a finite element representation of the equations of motion, with the movement of the free surface represented using the level set method, and has been implemented in SIERRA/ARIA. An empirically based time- and temperature-dependent density model is used to encapsulate the complex physics of foam nucleation and growth in a numerically tractable model. The change in density with time is at the heart of the foam self-expansion as it creates the motion of the foam. This continuum-level model uses an homogenized description of foam, which does not include the gas explicitly. Results from the model are compared to temperature-instrumented flow visualization experiments giving the location of the foam front as a function of time for our EFAR model system.

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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.

As part of an effort to reduce costs and improve quality control in encapsulation and potting processes the Technology Initiative Project ''Defect Free Manufacturing and Assembly'' has completed a computational modeling study of flows representative of those seen in these processes. Flow solutions are obtained using a coupled, finite-element-based, numerical method based on the GOMA/ARIA suite of Sandia flow solvers. The evolution of the free surface is solved with an advanced level set algorithm. This approach incorporates novel methods for representing surface tension and wetting forces that affect the evolution of the free surface. In addition, two commercially available codes, ProCAST and MOLDFLOW, are also used on geometries representing encapsulation processes at the Kansas City Plant. Visual observations of the flow in several geometries are recorded in the laboratory and compared to the models. Wetting properties for the materials in these experiments are measured using a unique flowthrough goniometer.

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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 Newton's method with analytic or numerical sensitivities, fully-coupled Newton-Krylov methods, fully-coupled Picard's 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 Aria's more advanced capabilities. Aria is based on the Sierra Framework.

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To reduce costs and hazardous wastes associated with the production of lead-based active ceramic components, an injection molding process is being investigated to replace the current machining process. Here, lead zirconate titanate (PZT) ceramic particles are suspended in a thermoplastic resin and are injected into a mold and allowed to cool. The part is then bisque fired and sintered to complete the densification process. To help design this new process we use a finite element model to describe the injection molding of the ceramic paste. Flow solutions are obtained using a coupled, finite-element based, Newton-Raphson numerical method based on the GOMA/ARIA suite of Sandia flow solvers. The evolution of the free surface is solved with an advanced level set algorithm. This approach incorporates novel methods for representing surface tension and wetting forces that affect the evolution of the free surface. Thermal, rheological, and wetting properties of the PZT paste are measured for use as input to the model. The viscosity of the PZT is highly dependent both on temperature and shear rate. One challenge in modeling the injection process is coming up with appropriate constitutive equations that capture relevant phenomenology without being too computationally complex. For this reason we model the material as a Carreau fluid and a WLF temperature dependence. Two-dimensional (2D) modeling is performed to explore the effects of the shear in isothermal conditions. Results indicate that very low viscosity regions exist near walls and that these results look similar in terms of meniscus shape and fill times to a simple Newtonian constitutive equation at the shear-thinned viscosity for the paste. These results allow us to pick a representative viscosity to use in fully three-dimensional (3D) simulation, which because of numerical complexities are restricted to using a Newtonian constitutive equation. Further 2D modeling at nonisothermal conditions shows that the choice of representative Newtonian viscosity is dependent on the amount of heating of the initially room temperature mold. An early 3D transient model shows that the initial design of the distributor is sub-optimal. However, these simulations take several months to run on 4 processors of an HP workstation using a preconditioner/solver combination of ILUT/GMRES with fill factors of 3 and PSPG stabilization. Therefore, several modifications to the distributor geometry and orientations of the vents and molds have been investigated using much faster 3D steady-state simulations. The pressure distribution for these steady-state calculations is examined for three different distributor designs to see if this can indicate which geometry has the superior design. The second modification, with a longer distributor, is shown to have flatter, more monotonic isobars perpendicular to the flow direction indicating a better filling process. The effects of the distributor modifications, as well as effects of the mold orientation, have also been examined with laboratory experiments in which the flow of a viscous Newtonian oil entering transparent molds is recorded visually. Here, the flow front is flatter and voids are reduced for the second geometry compared to the original geometry. A horizontal orientation, as opposed to the planned vertical orientation, results in fewer voids. Recently, the Navier-Stokes equations have been stabilized with the Dohrman-Bochev PSPP stabilization method, allowing us to calculate transient 3D simulations with computational times on the order of days instead of months. Validation simulations are performed and compared to the experiments. Many of the trends of the experiments are captured by the level set modeling, though quantitative agreement is lacking mainly due to the high value of the gas phase viscosity necessary for numerical stability, though physically unrealistic. More correct trends are predicted for the vertical model than the horizontal model, which is serendipitous as the actual mold is held in a vertical geometry. The full, transient mold filling calculations indicate that the flow front is flatter and voids may be reduced for the second geometry compared to the original geometry. The validated model is used to predict mold filling for the actual process with the material properties for the PZT paste, the original distributor geometry, and the mold in a vertical orientation. This calculation shows that voids may be trapped at the four corners of the mold opposite the distributor.

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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.

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Solidification and blood flow seemingly have little in common, but each involves a fluid in contact with a deformable solid. In these systems, the solid-fluid interface moves as the solid advects and deforms, often traversing the entire domain of interest. Currently, these problems cannot be simulated without innumerable expensive remeshing steps, mesh manipulations or decoupling the solid and fluid motion. Despite the wealth of progress recently made in mechanics modeling, this glaring inadequacy persists. We propose a new technique that tracks the interface implicitly and circumvents the need for remeshing and remapping the solution onto the new mesh. The solid-fluid boundary is tracked with a level set algorithm that changes the equation type dynamically depending on the phases present. This novel approach to coupled mechanics problems promises to give accurate stresses, displacements and velocities in both phases, simultaneously.