Derek Gaston

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.

Tightly Coupled Multiphysics Algorithms for Pebble Bed Reactors

Abstract We have developed a tightly coupled multiphysics simulation tool for the pebble bed reactor (PBR) concept, a specific type of very high temperature gas-cooled reactor. The simulation tool PRONGHORN takes advantage of the Multiphysics Object-Oriented Simulation Environment library and is capable of solving multidimensional thermal-fluid and neutronics problems implicitly with a Newton-based approach. Expensive Jacobian matrix formation is alleviated via the Jacobian-free Newton-Krylov method, and physics-based preconditioning is applied to minimize Krylov iterations. Motivation for the work is provided via analysis and numerical experiments on simpler multiphysics reactor models. We then provide detail of the physical models and numerical methods in PRONGHORN. Finally, PRONGHORN’s algorithmic capability is demonstrated on a number of PBR test cases.

Fully-coupled engineering and mesoscale simulations of thermal conductivity in UO2 fuel using an implicit multiscale approach

Though the thermal conductivity of solid UO2 is well characterized, its value is sensitive to microstructure changes. In this study, we propose a two-way coupling of a mesoscale phase field irradiation model to an engineering scale, finite element calculation to capture the microstructure dependence of the conductivity. To achieve this, the engineering scale thermomechanics system is solved in a parallel, fully-coupled, fully-implicit manner using the preconditioned Jacobian-free Newton Krylov (JFNK) method. Within the JFNK function evaluation phase of the calculation, the microstructure-influenced thermal conductivity is calculated by the mesoscale model and passed back to the engineering scale calculation. Initial results illustrate quadratic nonlinear convergence and good parallel scalability.

Parallel multiphysics algorithms and software for computational nuclear engineering

There is a growing trend in nuclear reactor simulation to consider multiphysics problems. This can be seen in reactor analysis where analysts are interested in coupled flow, heat transfer and neutronics, and in fuel performance simulation where analysts are interested in thermomechanics with contact coupled to species transport and chemistry. These more ambitious simulations usually motivate some level of parallel computing. Many of the coupling efforts to date utilize simple code coupling or first-order operator splitting, often referred to as loose coupling. While these approaches can produce answers, they usually leave questions of accuracy and stability unanswered. Additionally, the different physics often reside on separate grids which are coupled via simple interpolation, again leaving open questions of stability and accuracy. Utilizing state of the art mathematics and software development techniques we are deploying next generation tools for nuclear engineering applications. The Jacobian-free Newton-Krylov (JFNK) method combined with physics-based preconditioning provide the underlying mathematical structure for our tools. JFNK is understood to be a modern multiphysics algorithm, but we are also utilizing its unique properties as a scale bridging algorithm. To facilitate rapid development of multiphysics applications we have developed the Multiphysics Object-Oriented Simulation Environment (MOOSE). Examples from two MOOSE-based applications: PRONGHORN, our multiphysics gas cooled reactor simulation tool and BISON, our multiphysics, multiscale fuel performance simulation tool will be presented.

A Globally-Implicit Computational Framework for Physics-based Simulation of Coupled Thermo-Hydro-Mechanical Problems: Application to Sustainability of Geothermal Reservoirs

Numerical modeling has played an important role in understanding the behavior of geothermal systems since as early as the 1970s. While capabilities of geothermal reservoir simulators have grown since then, the prospect of simulating more challenging classes of geothermal problems–such as reservoir creation and operation of engineered geothermal systems (EGS), high enthalpy supercritical magmatic systems, etc–pose additional, and very significant, computational challenges that the current generation of continuum or dual-continuum hydrothermal models are ill-equipped to describe.