Abstract
In the previous chapter we saw that physical phenomena of interest to us can be described by a general scalar transport equation. In this chapter, we examine numerical methods for solving this type of equation and introduce the different numerical methods for mass transfer. We also explore how to characterize our numerical methods in terms of accuracy, consistency, stability, and convergence.
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References
Badalassi VE, Ceniceros HD, Banerjee S (2003) Computation of multiphase systems with phase field models. J Comput Phys 190(2):371–397
Benzi R, Biferale L, Sbragaglia M et al (2006) Mesoscopic modeling of a two-phase flow in the presence of boundaries: the contact angle. Phys Rev E 74(2). https://doi.org/10.1103/PhysRevE.74.021509
Cortis A, Berkowitz B (2004) Anomalous transport in “classical” soil and sand columns. Soil Sci Soc Am J 68(5):1539–1548
Gunstensen AK, Rothman DH (1991) Lattice Boltzmann model of immiscible fluids. Phys Rev A 43(8):4320–4327
He X, Chen S, Zhang R (1999) A Lattice Boltzmann scheme for incompressible multiphase flow and its application in simulation of Rayleigh-Taylor Instability. J Comput Phys 152:642–663
Huang H, Lu X-Y (2009) Relative permeabilities and coupling effects in steady-state gas-liquid flow in porous media: a lattice Boltzmann study. Phys Fluids 21(9):092104
Hysing S, Turek S, Kuzmin D et al (2009) Quantitative benchmark computations of two-dimensional bubble dynamics. Int J Numer Meth Fluids 60(11):1259–1288
Jacqmin D (1999) Calculation of two-phase Navier-Stokes flows using phase-field modeling. J Comput Phys 155(1):96–127
Kang Q, Zhang D, Chen S (2002) Displacement of a two-dimensional immiscible droplet in a channel. Phys Fluids 14(9):3203
Lenormand R, Touboul E, Zarcone C (1988) Numerical models and experiments on immiscible displacements in porous media. J Fluid Mech 189(1):165–187
Martys NS, Chen H (1996) Simulation of multicomponent fluids in complex three-dimensional geometries by the lattice Boltzmann method. Phys Rev E 53(1):743–751
Qian YH, D’Humières D, Lallemand P (1992) Lattice BGK models for Navier-Stokes equation. Europhys Lett 17(6):479–484
Shan X, Chen H (1993) Lattice Boltzmann model for simulating flows with multiple phases and components. Phys Rev E 47(3):1815–1820
Shan X, Chen H (1994) Simulation of nonideal gases and liquid-gas phase transitions by the lattice Boltzmann equation. Phys Rev E 49(4):2491–2498
Shan X, Doolen DG (1994) Multicomponent lattice-Boltzmann model with interparticle interaction. J Stat Phys 81(1–2):379–393
Swift MR, Osborn WR, Yeomans JM (1995) Lattice Boltzmann simulation of nonideal fluids. Phys Rev Lett 75(5):830–833
Swift MR, Orlandini E, Osborn WR et al (1996) Lattice Boltzmann simulations of liquid-gas and binary fluid systems. Phys Rev E 54(5):5041–5052
Toride N, Inoue M, Leij FJ (2003) Hydrodynamic dispersion in an unsaturated dune sand. Soil Sci Soc Am J 67(3):703–712
Toride N, Leij F, van Genuchten MT (1995) The CXTFIT code for estimating transport parameters from laboratory or filed tracer experiments. US Salinity Laboratory Riverside, Riverside
van Genuchten MT, Wierenga P (1976) Mass transfer studies in sorbing porous media I. Analytical solutions. Soil Sci Soc Am J 40(4):473–480
Villanueva W, Amberg G (2006) Some generic capillary-driven flows. Int J Multiph Flow 32(9):1072–1086
Yue P, Feng JJ, Liu C et al (2004) A diffuse-interface method for simulating two-phase flows of complex fluids. J Fluid Mech 515:293–317
Zhuang L, Raoof A, Mahmoodlu MG et al (2021) Unsaturated flow effects on solute transport in porous media. J Hydrol 598:126301
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Dou, Z., Zhou, Z., Wang, J., Huang, Y. (2024). Numerical Methods of Mass Transfer Process in Fractured Media. In: Mass Transfer Dynamics of Contaminants in Fractured Media. Springer, Singapore. https://doi.org/10.1007/978-981-99-9187-7_6
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DOI: https://doi.org/10.1007/978-981-99-9187-7_6
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