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

Journal Article · Tue Sep 01 00:00:00 EDT 2015 · Annals of Nuclear Energy (Oxford)

DOI:https://doi.org/10.1016/j.anucene.2015.04.016· OSTI ID:1184716

Zou, Ling ^[1]; Zhao, Haihua ^[1]; Zhang, Hongbin ^[1]

---

1. Idaho National Lab. (INL), Idaho Falls, ID (United States)

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.

• Research Organization: Idaho National Lab. (INL), Idaho Falls, ID (United States)
• Sponsoring Organization: USDOE Office of Nuclear Energy (NE)
• DOE Contract Number: AC07-05ID14517
• OSTI ID: 1184716
• Report Number(s): INL/JOU-14-33485; TRN: US1500201
• Journal Information: Annals of Nuclear Energy (Oxford), Vol. 83, Issue C; ISSN 0306-4549
• Publisher: Elsevier
• Country of Publication: United States
• Language: English

Related Subjects

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