Publications

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We present an error estimation method for immersed interface solutions of elliptic boundary value problems. As opposed to an asymptotic rate that indicates how the errors in the numerical method converge to zero, we seek a posteriori estimates of the errors, and their spatial distribution, for a given solution. Our estimate is based upon the classical idea of defect corrections, which requires the application of a higher-order discretization operator to a solution achieved with a lower-order discretization. Our model problem will be an elliptic boundary value problem in which the coefficients are discontinuous across an internal boundary.

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Numerical modeling is increasingly becoming an indispensable tool for investigations in many fields of physics. Such modeling is especially useful in today's big science projects as a tool that can provide predictions and design parameters. The reliability of simulation results is thus essential. Code-to-code comparisons can help increase our confidence in simulation results, especially when other verification methods - such as comparison to theoretical models or experimental results - are limited or unavailable. In this paper, we describe a code-to-code comparison exercise wherein we compare one-dimensional vacuum arc discharge simulation results from two independent particle-in-cell (PIC) codes. As part of our case study, we define a vacuum arc discharge test problem that can be used by other research groups for further comparison. Early disagreement between the two sets of our results motivated us to re-examine the underlying methods in our codes. After remedying discrepancies, we observe good agreement in vacuum arc discharge time-to-breakdown, as well as in the time evolution of particle and current densities. This exercise demonstrates the usefulness of code-to-code comparisons and provides an example case study for the benefit of other research groups who may wish to carry out similar code-to-code comparisons. © 2012 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Multilayer coextrusion has become a popular commercial process for producing complex polymeric products from soda bottles to reflective coatings. A numerical model of a multilayer coextrusion process is developed based on a finite element discretization and two different free-surface methods, an arbitrary-Lagrangian-Eulerian (ALE) moving mesh implementation and an Eulerian level set method, to understand the moving boundary problem associated with the polymer-polymer interface. The goal of this work is to have a numerical capability suitable for optimizing and troubleshooting the coextrusion process, circumventing flow instabilities such as ribbing and barring, and reducing variability in layer thickness. Though these instabilities can be both viscous and elastic in nature, for this work a generalized Newtonian description of the fluid is used. Models of varying degrees of complexity are investigated including stability analysis and direct three-dimensional finite element free surface approaches. The results of this work show how critical modeling can be to reduce build test cycles, improve material choices, and guide mold design.

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This report summarizes the work completed during FY2007 and FY2008 for the LDRD project ''Hybrid Plasma Modeling''. The goal of this project was to develop hybrid methods to model plasmas across the non-continuum-to-continuum collisionality spectrum. The primary methodology to span these regimes was to couple a kinetic method (e.g., Particle-In-Cell) in the non-continuum regions to a continuum PDE-based method (e.g., finite differences) in continuum regions. The interface between the two would be adjusted dynamically ased on statistical sampling of the kinetic results. Although originally a three-year project, it became clear during the second year (FY2008) that there were not sufficient resources to complete the project and it was terminated mid-year.

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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.