David Andrs

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.

RELAP-7 Theory Manual

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

Preliminary Study on the Suitability of a Second-Order Reconstructed Discontinuous Galerkin Method for RELAP-7 Thermal-Hydraulic Modeling

This document presents a preliminary study on the suitability of a second-order reconstructed discontinuous Galerkin (rDG) method for RELAP-7 thermal-hydraulic modeling. The document begins with a brief description of the governing equations for compressible, two-phase vapor and liquid flow, with a presentation of the seven-equation formulation details. A comparative study between the second-order rDG method and the RELAP-7’s finite element method (FEM) with a entropy viscosity method (EVM) based numerical stabilization scheme (namely FEM-EVM) over a series of benchmark test problems is demonstrated. The intent for this suite of test problems is to provide baseline comparison data that demonstrate the performance of 1) the rDG solution and 2) the RELAP-7’s FEM-EVM solution (with RELAP-7 code version dated August 15, 2017), on problems from singleto specific, limited two-phase flows. For all the test problems in this document, the rDG solutions were obtained with a second-order, two-step, explicit strong stability preserving Runge-Kutta time integration method. The computational results clearly indicate that the performance of the rDG method is superior to that of the RELAP-7’s FEM-EVM method in all the test problems presented. Therefore, as far as the test problems in this document are considered, the second-order rDG method is recommended as an improved solution method option for RELAP-7.

RELAP-7 Progress Report. FY-2015 Optimization Activities Summary

This report summarily documents the optimization activities on RELAP-7 for FY-2015. It includes the migration from the analytical stiffened gas equation of state for both the vapor and liquid phases to accurate and efficient property evaluations for both equilibrium and metastable (nonequilibrium) states using the Spline-Based Table Look-up (SBTL) method with the IAPWS-95 properties for steam and water. It also includes the initiation of realistic closure models based, where appropriate, on the U.S. Nuclear Regulatory Commission’s TRACE code. It also describes an improved entropy viscosity numerical stabilization method for the nonequilibrium two-phase flow model of RELAP-7. For ease of presentation to the reader, the nonequilibrium two-phase flow model used in RELAP-7 is briefly presented, though for detailed explanation the reader is referred to RELAP-7 Theory Manual [R.A. Berry, J.W. Peterson, H. Zhang, R.C. Martineau, H. Zhao, L. Zou, D. Andrs, “RELAP-7 Theory Manual,” Idaho National Laboratory INL/EXT-14-31366(rev. 1), February 2014].

Refined Boiling Water Reactor Station Blackout Simulation with RELAP-7

This is a DOE milestone report to demonstrate refined BWR SBO simulations with the RELAP-7 code.

RELAP-7 User's Guide

The document contains a users guide on how to run the RELAP-7 code. The RELAP-7 code is the next generation nuclear reactor system safety analysis code being developed at the Idaho National Laboratory. RELAP-7 will become the main reactor systems simulation toolkit for the LWRS (Light Water Reactor Sustainability) program’s RISMC (Risk Informed Safety Margin Characterization) effort and the next generation tool in the RELAP reactor safety/systems analysis application series. RELAP-7 is written with object oriented programming language C++. A number of example problems and their associated input files are presented in this document to guide users to run the RELAP-7 code starting with simple pipe problems to problems with increasing complexity.

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.