John W. Peterson

A quantitative comparison between C0 and C1 elements for solving the Cahn-Hilliard equation

The Cahn-Hilliard (CH) equation is a time-dependent fourth-order partial differential equation (PDE). When solving the CH equation via the finite element method (FEM), the domain is discretized by C^1-continuous basis functions or the equation is split into a pair of second-order PDEs, and discretized via C^0-continuous basis functions. In the current work, a quantitative comparison between C^1 Hermite and C^0 Lagrange elements is carried out using a continuous Galerkin FEM formulation. The different discretizations are evaluated using the method of manufactured solutions solved with Newtons method and Jacobian-Free Newton Krylov. It is found that the use of linear Lagrange elements provides the fastest computation time for a given number of elements, while the use of cubic Hermite elements provides the lowest error. The results offer a set of benchmarks to consider when choosing basis functions to solve the CH equation. In addition, an example of microstructure evolution demonstrates the different types of elements for a traditional phase-field model.

Rapid multiphase-field model development using a modular free energy based approach with automatic differentiation in MOOSE/MARMOT

Abstract We present a novel phase-field model development capability in the open source MOOSE finite element framework. This facility is based on the “modular free energy” approach in which the phase-field equations are implemented in a general form that is logically separated from model-specific data such as the thermodynamic free energy density and mobility functions. Free energy terms contributing to a phase-field model are abstracted into self-contained objects that can be dynamically combined at simulation run time. Combining multiple chemical and mechanical free energy contributions expedites the construction of coupled phase-field, mechanics, and multiphase models. This approach allows computational material scientists to focus on implementing new material models, and to reuse existing solution algorithms and data processing routines. A key new aspect of the rapid phase-field development approach that we discuss in detail is the automatic symbolic differentiation capability. Automatic symbolic differentiation is used to compute derivatives of the free energy density functionals, and removes potential sources of human error while guaranteeing that the nonlinear system Jacobians are accurately approximated. Through just-in-time compilation, we greatly reduce the computational expense of evaluating the differentiated expressions. The new capability is demonstrated for a variety of representative applications.

RELAP-7 Theory Manual

This document summarizes the physical models and mathematical formulations used in the RELAP-7 code.

Improved pressurized Marinelli beaker measurements of radioactive xenon in air.

INL has shown that a Marinelli beaker geometry can be used for the measurement of radioactive xenon in air using an aluminum Marinelli. A carbon fiber Marinelli was designed and constructed to improve overall performance. This composite Marinelli can withstand sample pressures of 276bar and achieve approximately a 4x performance improvement in the minimum detectable concentrations (MDCs) and concentration uncertainties. The MDCs obtained during a 24h assay for 133Xe, 131mXe, and 135Xe are: 1.4, 13, and 0.35Bq/m3.

Report on Evaluation, Verification, and Assessment of Porosity Migration Model in Fast Reactor MOX Fuel

This report documents the progress of simulating pore migration in ceramic (UO2 and mixed oxide or MOX) fuel using BISON. The porosity field is treated as a function of space and time whose evolution is governed by a custom convection-di↵usion-reaction equation (described here) which is coupled to the heat transfer equation via the temperature field. The porosity is initialized to a constant value at every point in the domain, and as the temperature (and its gradient) are increased by application of a heat source, the pores move up the thermal gradient and accumulate at the center of the fuel in a time-frame that is consistent with observations from experiments. There is an inverse dependence of the fuel’s thermal conductivity on porosity (increasing porosity decreases thermal conductivity, and vice-versa) which is also accounted for, allowing the porosity equation to couple back into the heat transfer equation. Results from an example simulation are shown to demonstrate the new capability.

RELAP-7: Demonstrating the integration of two-phase flow components for an ideal BWR loop

This is DOE Level 3 milestone report documenting RELAP-7s capability to simulate an ideal BWR loop.