表征体元尺度渗流的离散统一动理学格式
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摘要
结合表征体元尺度的通用渗流模型,提出离散统一动理学格式(DUGKS)渗流方法,分别用均匀网格和非均匀网格计算二维Poiseuille、 Couette、方腔流等经典渗流问题,检验DUGKS渗流方法的有效性和非均匀网格应用的优势,将DUGKS渗流方法应用到裂缝系统中.
DUGKS is extended to model porous media flow at representative elementary volume scale combined with generalized porous media model. It is verified by several two-dimensional classical problems: Poiseuille flow, Couette flow and cavity flow. Effectiveness of DUGKS for porous media flow is tested and advantage of DUGKS in grid flexibility is demonstrated. A fracture system is modeled by DUGKS for porous media flow.
DUGKS is extended to model porous media flow at representative elementary volume scale combined with generalized porous media model. It is verified by several two-dimensional classical problems: Poiseuille flow, Couette flow and cavity flow. Effectiveness of DUGKS for porous media flow is tested and advantage of DUGKS in grid flexibility is demonstrated. A fracture system is modeled by DUGKS for porous media flow.
引文
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[18] KANG Q,ZHANG D,CHEN S.Unified lattice Boltzmann method for flow in multiscale porous media[J].Physical Review E,2002,66(5):056307.
[19] ZHU L,WANG P,GUO Z.Performance evaluation of the general characteristics based off-lattice Boltzmann scheme and DUGKS for low speed continuum flows[J].Journal of Computational Physics,2017,333:227-246.
[20] ERGUN S.Fluid flow through packed columns[J].Chem Eng Prog,1952,48:89-94.
[21] WU C,SHI B,CHAI Z,et al.Discrete unified gas kinetic scheme with a force term for incompressible fluid flows[J].Computers & Mathematics with Applications,2016,71(12):2608-2629.
[22] HE X,CHEN S,DOOLEN G D.A novel thermal model for the lattice Boltzmann method in incompressible limit[J].Journal of Computational Physics,1998,146(1):282-300.
[23] HUANG Z,YAO J,WANG Y,et al.Numerical simulation on water flooding development of fractured reservoirs in a discrete-fracture model[J].Chinese Journal of Computational Physics,2011,28(1):41-49.
[24] ZHANG J,HUANG S,CHENG L.Monte Carlo calculation of stable productivity of fractured directional wells in natural fracture reservoirs[J].Chinese Journal of Computational Physics,2014,31(5):567-572.
[2] BRINKMAN H.A calculation of the viscous force exerted by a flowing fluid on a dense swarm of particles[J].Applied Scientific Research,1949,1(1):27-34.
[3] VAFAI K,TIEN C.Boundary and inertia effects on flow and heat transfer in porous media[J].International Journal of Heat and Mass Transfer,1981,24(2):195-203.
[4] WHITAKER S.The Forchheimer equation:A theoretical development[J].Transport in Porous Media,1996,25(1):27-61.
[5] NITHIARASU P,SEETHARAMU K,SUNDARARAJAN T.Natural convective heat transfer in a fluid saturated variable porosity medium[J].International Journal of Heat and Mass Transfer,1997,40(16):3955-3967.
[6] KARIMIFARD M,CHARRIERMOJTABI M C,VAFAI K.Non-Darcian effects on double-diffusive convection within a porous medium[J].Numerical Heat Transfer Part A:Applications,1997,31(8):837-852.
[7] JUE T C.Analysis of heat and fluid flow in partially divided fluid saturated porous cavities[J].Heat and Mass Transfer,2000,36(4):285-294.
[8] 郭照立,郑楚光.格子 Boltzmann方法的原理及应用[M].北京:科学出版社,2009.
[9] CHEN S,DOOLEN G D.Lattice Boltzmann method for fluid flows[J].Annual Review of Fluid Mechanics,1998,30(1):329-364.
[10] SUCCI S.The lattice Boltzmann equation:For fluid dynamics and beyond[M].Oxford University Press,2001.
[11] GUO Z,ZHAO T.Lattice Boltzmann model for incompressible flows through porous media[J].Physical Review E,2002,66(3):036304.
[12] ZARGHAMI A,BISCARINI C,SUCCI S,et al.Hydrodynamics in porous media:A finite volume lattice Boltzmann study[J].Journal of Scientific Computing,2014,59(1):80-103.
[13] GUO Z,XU K,WANG R.Discrete unified gas kinetic scheme for all Knudsen number flows:Low-speed isothermal case[J].Physical Review E,2013,88(3):033305.
[14] GUO Z,WANG R,XU K.Discrete unified gas kinetic scheme for all Knudsen number flows II:Thermal compressible case[J].Physical Review E,2015,91(3):033313.
[15] XU K.A gas-kinetic BGK scheme for the Navier-Stokes equations and its connection with artificial dissipation and Godunov method[J].Journal of Computational Physics,2001,171(1):289-335.
[16] ZHU L,GUO Z,XU K.Discrete unified gas kinetic scheme on unstructured meshes[J].Computers & Fluids,2016,127:211-225.
[17] WANG P,ZHU L,GUO Z,et al.A comparative study of LBE and DUGKS methods for nearly incompressible flows[J].Communications in Computational Physics,2015,17(3):657-681.
[18] KANG Q,ZHANG D,CHEN S.Unified lattice Boltzmann method for flow in multiscale porous media[J].Physical Review E,2002,66(5):056307.
[19] ZHU L,WANG P,GUO Z.Performance evaluation of the general characteristics based off-lattice Boltzmann scheme and DUGKS for low speed continuum flows[J].Journal of Computational Physics,2017,333:227-246.
[20] ERGUN S.Fluid flow through packed columns[J].Chem Eng Prog,1952,48:89-94.
[21] WU C,SHI B,CHAI Z,et al.Discrete unified gas kinetic scheme with a force term for incompressible fluid flows[J].Computers & Mathematics with Applications,2016,71(12):2608-2629.
[22] HE X,CHEN S,DOOLEN G D.A novel thermal model for the lattice Boltzmann method in incompressible limit[J].Journal of Computational Physics,1998,146(1):282-300.
[23] HUANG Z,YAO J,WANG Y,et al.Numerical simulation on water flooding development of fractured reservoirs in a discrete-fracture model[J].Chinese Journal of Computational Physics,2011,28(1):41-49.
[24] ZHANG J,HUANG S,CHENG L.Monte Carlo calculation of stable productivity of fractured directional wells in natural fracture reservoirs[J].Chinese Journal of Computational Physics,2014,31(5):567-572.