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Title: Applications of high-resolution spatial discretization scheme and Jacobian-free Newton–Krylov method in two-phase flow problems

The majority of the existing reactor system analysis codes were developed using low-order numerical schemes in both space and time. In many nuclear thermal–hydraulics applications, it is desirable to use higher-order numerical schemes to reduce numerical errors. High-resolution spatial discretization schemes provide high order spatial accuracy in smooth regions and capture sharp spatial discontinuity without nonphysical spatial oscillations. In this work, we adapted an existing high-resolution spatial discretization scheme on staggered grids in two-phase flow applications. Fully implicit time integration schemes were also implemented to reduce numerical errors from operator-splitting types of time integration schemes. The resulting nonlinear system has been successfully solved using the Jacobian-free Newton–Krylov (JFNK) method. The high-resolution spatial discretization and high-order fully implicit time integration numerical schemes were tested and numerically verified for several two-phase test problems, including a two-phase advection problem, a two-phase advection with phase appearance/disappearance problem, and the water faucet problem. Numerical results clearly demonstrated the advantages of using such high-resolution spatial and high-order temporal numerical schemes to significantly reduce numerical diffusion and therefore improve accuracy. Our study also demonstrated that the JFNK method is stable and robust in solving two-phase flow problems, even when phase appearance/disappearance exists.
Authors:
 [1] ;  [1] ;  [1]
  1. Idaho National Lab. (INL), Idaho Falls, ID (United States)
Publication Date:
OSTI Identifier:
1184716
Report Number(s):
INL/JOU--14-33485
Journal ID: ISSN 0306-4549; TRN: US1500201
DOE Contract Number:
AC07-05ID14517
Resource Type:
Journal Article
Resource Relation:
Journal Name: Annals of Nuclear Energy (Oxford); Journal Volume: 83; Journal Issue: C
Publisher:
Elsevier
Research Org:
Idaho National Laboratory (INL), Idaho Falls, ID (United States)
Sponsoring Org:
USDOE Office of Nuclear Energy (NE)
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICS AND COMPUTING; 42 ENGINEERING; 22 GENERAL STUDIES OF NUCLEAR REACTORS; TWO-PHASE FLOW; WATER FAUCETS; RESOLUTION; THERMAL HYDRAULICS; ADVECTION; ACCURACY; COORDINATES; NONLINEAR PROBLEMS; SYSTEMS ANALYSIS; CALCULATION METHODS; NUMERICAL SOLUTION JACOBIAN-FREE-KRYLOV METHOD; HIGH-RESOLUTION SPATIAL DISCRETIZATION SCHEME; STAGGERED GRID; IMPLICIT SCHEME