×

Energy-consistent formulation of the pressure-free two-fluid model. (English) Zbl 07847161

MSC:

76-XX Fluid mechanics
65-XX Numerical analysis

References:

[1] WallisGB. One‐Dimensional Two‐Phase Flow. McGraw‐Hill; 1969.
[2] GoldszalA, DanielsonTJ, BansalKM, YangZL, JohansenST, DepayG. LedaFlow 1D: simulation results with multiphase gas/condensate and oil/gas field data. Proceedings of the 13th International Conference on Multiphase Production Technology; 2007:17‐31; BHR Group, Edinburgh, UK.
[3] AursandP, HammerM, MunkejordST, WilhelmsenØ. Pipeline transport of CO2 mixtures: models for transient simulation. Int J Greenhouse Gas Control. 2013;15:174‐185. doi:10.1016/j.ijggc.2013.02.012
[4] BerryRA, ZouL, ZhaoH, et al. RELAP‐7 theory manual. Technical report INL/EXT‐14‐31366, Idaho National Laboratory, Idaho Falls, Idaho; 2014.
[5] BarneaD, TaitelY. Kelvin‐Helmholtz stability criteria for stratified flow: viscous versus non‐viscous (inviscid) approaches. Int J Multiph Flow. 1993;19(4):639‐649. doi:10.1016/0301‐9322(93)90092‐9 · Zbl 1144.76345
[6] IssaRI, KempfMHW. Simulation of slug flow in horizontal and nearly horizontal pipes with the two‐fluid model. Int J Multiph Flow. 2003;29(1):69‐95. doi:10.1016/S0301‐9322(02)00127‐1 · Zbl 1136.76538
[7] KrasnopolskyBI, LukyanovAA. A conservative fully implicit algorithm for predicting slug flows. J Comput Phys. 2018;355:597‐619. doi:10.1016/j.jcp.2017.11.032 · Zbl 1380.76063
[8] MasellaJM, TranQH, FerreD, PauchonC. Transient simulation of two‐phase flows in pipes. Int J Multiph Flow. 1998;24(5):739‐755. doi:10.1016/S0301‐9322(98)00004‐4 · Zbl 1121.76459
[9] FailleI, HeintzéE. A rough finite volume scheme for modeling two‐phase flow in a pipeline. Comput Fluids. 1999;28(2):213‐241. doi:10.1016/S0045‐7930(98)00023‐1 · Zbl 0964.76050
[10] BarneaD, TaitelY. Interfacial and structural stability of separated flow. Int J Multiph Flow. 1994;20:387‐414. doi:10.1016/0301‐9322(94)90078‐7 · Zbl 1134.76488
[11] LiaoJ, MeiR, KlausnerJF. A study on the numerical stability of the two‐fluid model near ill‐posedness. Int J Multiph Flow. 2008;34(11):1067‐1087. doi:10.1016/j.ijmultiphaseflow.2008.02.010
[12] López de BertodanoM, FullmerW, ClausseA, RansomVH. Two‐Fluid Model Stability, Simulation and Chaos. Springer International Publishing; 2017. · Zbl 1374.76002
[13] LyczkowskiRW, GidaspowD, SolbrigCW, HughesED. Characteristics and stability analyses of transient one‐dimensional two‐phase flow equations and their finite difference approximations. Nucl Sci Eng. 1978;66(3):378‐396. doi:10.13182/NSE78‐4
[14] RansomVH, HicksDL. Hyperbolic two‐pressure models for two‐phase flow. J Comput Phys. 1984;53(1):124‐151. doi:10.1016/0021‐9991(84)90056‐1 · Zbl 0537.76070
[15] StewartHB, WendroffB. Two‐phase flow: models and methods. J Comput Phys. 1984;56(3):363‐409. doi:10.1016/0021‐9991(84)90103‐7 · Zbl 0596.76103
[16] DrewDA, PassmanSL. Theory of Multicomponent Fluids. Springer; 1999.
[17] DinhTN, NourgalievRR, TheofanousTG. Understanding the ill‐posed two‐fluid model. Proceedings of the 10th International Topical Meeting on Nuclear Reactor Thermal Hydraulics. NURETH10; 2003; Seoul, Korea.
[18] ChiapolinoA, SaurelR. Models and methods for two‐layer shallow water flows. J Comput Phys. 2018;371:1043‐1066. doi:10.1016/j.jcp.2018.05.034 · Zbl 1415.76061
[19] HolmåsH, SiraT, NordsveenM, LangtangenHP, SchulkesR. Analysis of a 1D incompressible two‐fluid model including artificial diffusion. IMA J Appl Math. 2008;73(4):651‐667. doi:10.1093/imamat/hxm066 · Zbl 1229.76062
[20] LouakedM, HanichL, ThompsonCP. Well‐posedness of incompressible models of two‐ and three‐phase flow. IMA J Appl Math. 2003;68:595‐620. doi:10.1093/imamat/68.6.595 · Zbl 1147.76621
[21] Omgba‐EssamaC. Numerical Modelling of Transient Gas‐Liquid Flows (Application to Stratified & Slug Flow Regimes). PhD thesis. Cranfield, UK: Cranfield University; 2004.
[22] AkselsenAH. Efficient Numerical Methods for Waves in One‐Dimensional Two‐Phase Pipe Flows. PhD thesis. Trondheim, Norway: Norwegian University of Science and Technology; 2016.
[23] KeyfitzB, SandersR, SeverM. Lack of hyperbolicity in the two‐fluid model for two‐phase incompressible flow. Discr Contin Dyn Syst B. 2003;3(4):541‐563. doi:10.3934/dcdsb.2003.3.541 · Zbl 1055.35074
[24] EtratiA, FrigaardIA. A two‐layer model for buoyant inertial displacement flows in inclined pipes. Phys Fluids. 2018;30(2):022107. doi:10.1063/1.5019366
[25] MilewskiP, TabakE, TurnerC, RosalesR, MenzaqueF. Nonlinear stability of two‐layer flows. Commun Math Sci. 2004;2(3):427‐442. doi:10.4310/CMS.2004.v2.n3.a5 · Zbl 1084.76031
[26] JonesAV, ProsperettiA. On the suitability of first‐order differential models for two‐phase flow prediction. Int J Multiph Flow. 1985;11(2):133‐148. doi:10.1016/0301‐9322(85)90041‐2 · Zbl 0587.76177
[27] SanderseB, BuistJFH, HenkesRAWM. A novel pressure‐free two‐fluid model for one‐dimensional incompressible multiphase flow. J Comput Phys. 2021;426:109919. doi:10.1016/j.jcp.2020.109919 · Zbl 07510045
[28] BuistJFH, SanderseB, DubinkinaS, HenkesRAWM, OosterleeCW. Energy‐conserving formulation of the two‐fluid model for incompressible two‐phase flow in channels and pipes. Comput Fluids. 2022;244:105533. doi:10.1016/j.compfluid.2022.105533 · Zbl 1521.76402
[29] van’tHofB, VeldmanAEP. Mass, momentum and energy conserving (MaMEC) discretizations on general grids for the compressible Euler and shallow water equations. J Comput Phys. 2012;231(14):4723‐4744. doi:10.1016/j.jcp.2012.03.005 · Zbl 1245.76074
[30] FjordholmUS, MishraS, TadmorE. Well‐balanced and energy stable schemes for the shallow water equations with discontinuous topography. J Comput Phys. 2011;230(14):5587‐5609. doi:10.1016/j.jcp.2011.03.042 · Zbl 1452.35149
[31] FjordholmUS. Energy conservative and stable schemes for the two‐layer shallow water equations. In: LiT (ed.), JiangS (ed.), eds. Hyperbolic Problems. Vol. 17 & 18 of Series in Contemporary Applied Mathematics. Co‐Published with Higher Education Press; 2012:414‐421. · Zbl 1402.76086
[32] IshiiM, MishimaK. Two‐fluid model and hydrodynamic constitutive relations. Nucl Eng Des. 1984;82(2‐3):107‐126. doi:10.1016/0029‐5493(84)90207‐3
[33] MontiniM. Closure Relations of the One‐Dimensional Two‐Fluid Model for the Simulation of Slug Flows. PhD thesis. London, UK: Imperial College London; 2011.
[34] SanderseB, SmithIE, HendrixMHW. Analysis of time integration methods for the compressible two‐fluid model for pipe flow simulations. Int J Multiph Flow. 2017;95:155‐174. doi:10.1016/j.ijmultiphaseflow.2017.05.002
[35] SanderseB, VeldmanAEP. Constraint‐consistent Runge-Kutta methods for one‐dimensional incompressible multiphase flow. J Comput Phys. 2019;384:170‐199. doi:10.1016/j.jcp.2019.02.001 · Zbl 1451.76133
[36] LteifR. Well‐balanced numerical resolution of the two‐layer shallow water equations under rigid‐lid with wet-dry fronts. Comput Fluids. 2022;235:105277. doi:10.1016/j.compfluid.2021.105277 · Zbl 1521.76450
[37] FjordholmU, MishraS, TadmorE. Energy preserving and energy stable schemes for the shallow water equations. In: CuckerF (ed.), PinkusA (ed.), ToddMJ (ed.), eds. Foundations of Computational Mathematics. Cambridge University Press; 2008:93‐139. · Zbl 1381.76236
[38] ButcherJ. Numerical Methods for Ordinary Differential Equations. Wiley; 2003. · Zbl 1040.65057
[39] FullmerWD, RansomVH, Lopez de BertodanoMA. Linear and nonlinear analysis of an unstable, but well‐posed, one‐dimensional two‐fluid model for two‐phase flow based on the inviscid Kelvin-Helmholtz instability. Nucl Eng Des. 2014;268:173‐184. doi:10.1016/j.nucengdes.2013.04.043
[40] ThorpeSA. Experiments on the instability of stratified shear flows: immiscible fluids. J Fluid Mech. 1969;39(1):25‐48. doi:10.1017/S0022112069002023
[41] ChurchillSW. Friction factor equation spans all fluid flow regimes. Chem Eng. 1977;84:91‐92.
[42] BonzaniniA, PicchiD, PoesioP. Simplified 1D incompressible two‐fluid model with artificial diffusion for slug flow capturing in horizontal and nearly horizontal pipes. Energies. 2017;10(9):1372. doi:10.3390/en10091372
[43] BouchutF, ZeitlinV. A robust well‐balanced scheme for multi‐layer shallow water equations. Discr Contin Dyn Syst B. 2010;13(4):739. doi:10.3934/dcdsb.2010.13.739 · Zbl 1308.76060
[44] Castro‐DíazMJ, Fernández‐NietoED, González‐VidaJM, Parés‐MadroñalC. Numerical treatment of the loss of hyperbolicity of the two‐layer shallow‐water system. J Sci Comput. 2011;48(1):16‐40. doi:10.1007/s10915‐010‐9427‐5 · Zbl 1416.76140
[45] HamFE, LienFS, StrongAB. A fully conservative second‐order finite difference scheme for incompressible flow on nonuniform grids. J Comput Phys. 2002;177(1):117‐133. doi:10.1006/jcph.2002.7006 · Zbl 1066.76044
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.