ESTIMATION OF DISCRETIZATION ERROR FOR THREE DIMENSIONAL CFD SIMULATIONS USING A TAYLOR SERIES MODIFIED EQUATION ANALYSIS

Abstract

The Consortium for Advanced Simulation of LightWater Reactors (CASL) is working towards developing a virtual reactor called the Virtual Environment for Reactor Application (VERA). As part of this work, computational fluid dynamics (CFD) simulations are being made to inform lower fidelity models to predict heat transfer and fluid flow through a light water reactor core. A 5x5 fuel rod assembly with mixing vanes was chosen to represent a 17x17 fuel rod assembly. Even with this simplified geometry, it is estimated that hundreds of millions of cells are needed for a solution to be close to the asymptotic region. The large number of cells is an issue when completing solution verification studies because of computational cost.

Solution verification studies traditionally involve the use of Roache’s grid convergence index (GCI) to estimate the error, but require the solution to be in the asymptotic region. This is a severely limiting restriction for simulations with large range of length scales as is the case with the 5x5 fuel rod assembly with mixing vanes. Unfortunately, GCI does not perform well when the solution is outside the asymptotic region. However, a new method called the robust multi-regression (RMR) solution verification method has the potential to produce good results, even when the solution is outside the asymptotic region.

This study builds a software framework that improves the RMR solution verification analysis by improving the error model used to estimate the discretization error. Previous RMR work used a power function to model the error, which was the same function used in the Richardson extrapolation. The power function form is a result of a Taylor series expansion on a uniform grid for simple numerical schemes and physics. It can be improved by completing a Taylor series expansion for the numerical scheme, boundary conditions, and physics that are being employed in the simulation of interest. This framework was shown to improve the ability for the error model to estimate the discretization error and uncertainty. The improved error model was able to predict error on a refined grid within the uncertainty bounds, while the standard error model did not. In addition, the method of manufactured modified equation analysis solutions (MMMEAS) was developed and applied to justify the use of a down selection method for terms in the error model.