Computational methods lattice Boltzmann simulation

Rock properties are computed from the micro, to plug and whole core scale. The absolute permeability, for example, can be computed using Lattice-Boltzmann simulations, while the calculation of the formation resistivity factor is based on a solution of the Laplace equation with charge conservation. The elastic properties are calculated with the finite element method. 

Abstract In this chapter, the mesoscale computational methodology. Lattice Boltzmann Method (LBM), is introduced for the simulation of the interfacial Marangoni and Rayleigh elfects as described and discussed in Chap. 8. The fundamentals of LBM are briefly introduced and discussed. By the simulation using the LBM, some mechanisms and phenomena of the interfacial effect are studied, including the patterns of the interfacial disturbance for inducing the interfacial convections, conditions of initiating interfacial instability and interfacial convection as well as the effect on interfacial mass transfer. 

The flow resistance behavior of the reconstructed medium can now be examined by performing 3D flow simulations with the Lattice Boltzmann method (Chen and Doolen, 1998), and obtaining the permeability of the material (Konstandopoulos, 2003). Figure 8(a) depicts a visualization of 3D flow tubes and flow velocity distributions at different cross sections in a reconstructed filter material. Figure 8(b) shows the comparison of computer simulated and experimental permeabilities obtained with the experimental protocol described in Konstandopoulos (2003). 

During the past few decades, various theoretical models have been developed to explain the physical properties and to find key parameters for the prediction of the system behaviors. Recent technological trends focus toward integration of subsystem models in various scales, which entails examining the nanophysical properties, subsystem size, and scale-specified numerical analysis methods on system level performance. Multi-scale modeling components including quantum mechanical (i.e., density functional theory (DFT) and ab initio simulation), atom-istic/molecular (i.e., Monte Carlo (MC) and molecular dynamics (MD)), mesoscopic (i.e., dissipative particle dynamics (DPD) and lattice Boltzmann method (LBM)), and macroscopic (i.e., LBM, computational... 

Simulation techniques suitable for the description of phenomena at each length-scale are now relatively well established Monte Carlo (MC) and Molecular Dynamics (MD) methods at the molecular length-scale, various mesoscopic simulation methods such as Dissipative Particle Dynamics (Groot and Warren, 1997), Brownian Dynamics, or Lattice Boltzmann in the colloidal domain, Computational Fluid Dynamics at the continuum length-scale, and sequential-modular or equation-based methods at the unit operation/process-systems level. 

Only a few LES simulations have been reported describing the turbulent flow in single phase stirred tanks (e.g., [20, 77, 18]). The lattice-Boltzmann method is used in the more recent publications since this scheme is considered to be an efficient Navier-Stokes solver. Nevertheless, the computational requirements of these models are still prohibitive, therefore the application of this approach is restricted to academic research. No direct simulations of these vessels have been performed yet. 

The lattice Boltzmann method is a mesoscopic simulation method for complex fluid systems. The fluid is modeled as fictitious particles, and they propagate and coUide over a discrete lattice domain at discrete time steps. Macroscopic continuum equations can be obtained from this propagation-colhsion dynamics through a mathematical analysis. The particulate nature and local d3mamics also provide advantages for complex boundaries, multiphase/multicomponent flows, and parallel computation. 

The lattice Boltzmann method (LBM) is a relatively new simulation technique for complex fluid systems and has attracted great interests from researchers in computational physics and engineering. Unlike traditional computation fluid dynamics (CFD) methods to numerically solve the conservation equations of macroscopic properties (i.e., mass, momentum, and energy), LBM models the fluid as fictitious particles, and such particles perform consecutive propagation and collision processes over a discrete lattice mesh. Due to its particulate nature and local dynamics, LBM has several advantages over conventional CFD methods, especially in dealing with complex boundaries, incorporation of microscopic interactions, and parallel computation [1, 2]. 

Chen S., Chen H., Martinez D. Matthaeus W. (1991). Lattice Boltzmann model for simulation of magnetohydrodinamics. Physical Review Letter, 67(27), pp. 3776-3779. Chen S., Dawson S. P., Doolen G. D., Janecky D. R. Lawniczak A. (1995). Lattice methods and their applications to reacting systems. Comput. Chem. Eng 19(6-7), pp. 617-646. 

Meinhart, Simulation of fluid slip at 3D hydrophobic walls by the lattice Boltzmann method, J. Comput. Phys.. 

A possible solution for simulating transport processes in larger domains can be the lattice Boltzmann approach see, for example, [11, 12]. The great advantage of this method is that it allows for a massive parallelization of the implementation, which permits computation on large domains. 

The lattice Boltzmann method (LBM) is a relatively new simulation technique for complex fluid systems which has attracted a great deal of interest from researchers in computational physics. Unlike the traditional computation fluid dynamics (CFD), which numerically solves the conservation equations of macroscopic properties (i. e., mass. 

Lu, Z., Liao, Y., McLaughlin, J.B., Derksen, J.J., and Kostomaris, K. (2002) Large eddy simulations of a stirred tank using the lattice Boltzmann method on a nonuniform grid. / Comput. Phys., 181, 675 -704,... 

Saffman PG (1965) The lift on a small sphere in a slow shear flow. J Ruid Mech 22 385-400 Schlauch E, Ernst M, Seto R, Briesen H, Sommerfeld M, Behr M (2013) Comparison of three simulation methods for colloidal aggregates in Stokes flow finite elements, lattice Boltzmann and Stokesian dynamics. Comput Huids 86 199-209... 

Thbmmes G, Becker J, Junk M, Vaikuntam AK, Kehrwald D, Klar A, Steiner K, Wiegmann A (2009) A lattice Boltzmann method for immiscible multiphase flow simulations using the level set method. J Comput Phys 228 1139-1156... 

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