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.
Subject
Solution VerificationUncertainty Quantification
Discretization Error
Truncation Error
Modified Equation Analysis
Citation
Krueger, Aaron Martin (2017). ESTIMATION OF DISCRETIZATION ERROR FOR THREE DIMENSIONAL CFD SIMULATIONS USING A TAYLOR SERIES MODIFIED EQUATION ANALYSIS. Master's thesis, Texas A & M University. Available electronically from https : / /hdl .handle .net /1969 .1 /169608.