Publications

Abstract not provided.

Abstract not provided.

Abstract not provided.

Abstract not provided.

Abstract not provided.

Abstract not provided.

Abstract not provided.

Abstract not provided.

Abstract not provided.

Abstract not provided.

Abstract not provided.

Abstract not provided.

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.

Abstract not provided.

Abstract not provided.

Abstract not provided.

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.

Abstract not provided.

Abstract not provided.

Abstract not provided.

Abstract not provided.

Abstract not provided.

Abstract not provided.

Abstract not provided.