A preconditioned Krylov method for solution of the multi-dimensional, two ¯uid hydrodynamics equations T.J. Downar a, *,H.G.Joo b a School of Nuclear Engineering Purdue University, 1290 Nuclear Engineering Biulding, W. Lafayette, IN 47907, USA b Korea Atomic Energy Research Institute, PO Box 105, Yusong, Taejon, South Korea Received 6 July 1999; received in revised form 21 September 2000; accepted 15 October 2000 Abstract ApreconditionedKrylovmethodisintroducedforreducingthecomputationalburdeninthe solutionofthemulti-dimensional,two¯uidhydrodynamicsequations.TheBILU3Dprecondi- tionedBICGSTABmethodwasappliedtothelinearizedcontinuityequationintheinneritera- tionofthefullyimplicitsolutionofthemass,energy,andmomentumequationsintheEPRIcode VIPRE-02. A nuclear reactor thermal-hydraulics test problem was performed with 104 multi- dimensional¯owchannelsinthevessel.ForthesimulationofatypicalpressurizedwaterReactor steamlinebreaktransient,theoverallexecutiontimewasreducedbymorethan50%compared to the existing solution techniques which utilize stationary alternate direction implicit (ADI) iterativemethodsfortheinneriteration. # 2001ElsevierScienceLtd.Allrightsreserved. 1. Introduction The VIPRE-02 thermal-hydraulic analysis code models steady-state and opera- tional transient conditions in light water reactor (LWR) cores and vessels. VIPRE- 02employsafullyimplicitsub-channelformulationandhasafullthree-dimensional representation of the core and lower plenum for both pressurized water reactor (PWR) and boiling water reactor (BWR) vessels. The mathematical modeling and solution methods in VIPRE-02 are described in detail in VIPRE-02 (1994) and Kelleyetal.(1994).Thecodehasundergoneextensivevalidationagainstbothsingle Annals of Nuclear Energy 28 (2001) 1251±1267 www.elsevier.com/locate/anucene 0306-4549/01/$ - see front matter # 2001 Elsevier Science Ltd. All rights reserved. PII:S0306-4549(00)00124-9 * Corresponding author. Tel.: +1-765-49-45752. E-mail address: thomas.j.downar.1@purdue.edu (T.J. Downar).