Consistent forcing scheme in the cascaded lattice Boltzmann method

In this paper, we give a more pellucid derivation for the cascaded lattice Boltzmann method (CLBM) based on a general multiple-relaxation-time (MRT) frame through defining a shift matrix. When the shift matrix is a unit matrix, the CLBM degrades into an MRT LBM. Based on this, a consistent forcing scheme is developed for the CLBM. The applicability of the non-slip rule, the second-order convergence rate in space and the property of isotropy for the consistent forcing scheme is demonstrated through the simulation of several canonical problems. Several other existing force schemes previously used in the CLBM are also examined. The study clarifies the relation between MRT LBM and CLBM under a general framework

Modeling incompressible thermal flows using a central-moment-based lattice Boltzmann method

In this paper, a central-moment-based lattice Boltzmann (CLB) method for incompressible thermal flows is proposed. In the method, the incompressible Navier-Stokes equations and the convection-diffusion equation for the temperature field are sloved separately by two different CLB equations. Through the Chapman-Enskog analysis, the macroscopic governing equations for incompressible thermal flows can be reproduced. For the flow field, the tedious implementation for CLB method is simplified by using the shift matrix with a simplified central-moment set, and the consistent forcing scheme is adopted to incorporate forcing effects. Compared with several D2Q5 multiple-relaxation-time (MRT) lattice Boltzmann methods for the temperature equation, the proposed method is shown to be better Galilean invariant through measuring the thermal diffusivities on a moving reference frame. Thus a higher Mach number can be used for convection flows, which decreases the computational load significantly. Numerical simulations for several typical problems confirm the accuracy, efficiency, and stability of the present method. The grid convergence tests indicate that the proposed CLB method for incompressible thermal flows is of second-order accuracy in space

The Rheology and Domestic Choice of the Concept of Negotiable Securities

The concept of negotiable securities is an important part of the basic theory of negotiable securities, and also the logical starting point of securities study. Negotiable securities have experienced many times of baptism from the concept doctrines whose purpose is to realize the legal and economic functions since it has been created in 19th century as an unique legal name of the continental legal system. However, the theories of commercial law of China do not do well in the study of the concept of negotiable securities, not to mention the basic study of unfixed security theory, so it isn’t conductive to developing the effectiveness of securities. By means of study on the rheology of negotiable securities concept, this paper analyzes the advantages and disadvantages of different concept doctrines and points out train of thought of the concept study of negotiable securities and its essential interpretation for theories of commercial law of China, which helps lay the foundation for theoretical study on negotiable securities

Conflict and Explanation About the Use of Negotiable Instrument Law of China for the Documentary Letter of Credit Draft

The documentary letter of credit draft, first of all, depends on compulsory procedure of bill of exchange, legal status of sides during negotiating bank registration, unconditional payment and endorsement with signature and stamp; it also depends on other questions and conflicts, occurred with the use of UCP600. The applicable of the documentary letter of credit draft suffered from negotiable instrument law in China and the international convention on the law. Through the analysis of bill legal interpretation rules and international law practice, the documentary letter of credit draft not only matches the bill of exchange, but also plays the role of bill of exchange with unconditional payment. This provides the logic basis for the documentary letter of credit draft to apply negotiable instrument law in China and forward the legal interpretation to resolve the conflict

Explanations on the Typification and Right Attribute of Commercial Securities

Different from bills, the nature of securities rights of bill of lading and warehouse receipts has always perplexed the academia. The reason is the lack of basic researches on the negotiable securities theories, which make scholars confined to specific legal departments and cannot see the complete picture. This paper analyzes bills of lading and warehouse receipts on the base of the theories of negotiable securities and bills, and clarifies their attribute of commercial securities. While affirming the attribute of debt securities, this paper advocates to admit the property rights of bills of lading and warehouse receipts through analyzing the theoretical disputes between their property rights and creditor’s rights. Combined with the issue that delivery of securities has the same potency with delivery of goods, this paper argues the nature of property debt securities of bills of lading and warehouse receipts in a developmental way

Mesoscopic model for soft flowing systems with tunable viscosity ratio

We propose a mesoscopic model of binary fluid mixtures with tunable viscosity ratio based on the two-range pseudo-potential lattice Boltzmann method, for the simulation of soft flowing systems. In addition to the short range repulsive interaction between species in the classical single-range model, a competing mechanism between the short range attractive and mid-range repulsive interactions is imposed within each species. Besides extending the range of attainable surface tension as compared with the single-range model, the proposed scheme is also shown to achieve a positive disjoining pressure, independently of the viscosity ratio. The latter property is crucial for many microfluidic applications involving a collection of disperse droplets with a different viscosity from the continuum phase. As a preliminary application, the relative effective viscosity of a pressure-driven emulsion in a planar channel is computed.Comment: 14page

Unified lattice Boltzmann method with improved schemes for multiphase flow simulation: Application to droplet dynamics under realistic conditions

As a powerful mesoscale approach, the lattice Boltzmann method (LBM) has been widely used for the numerical study of complex multiphase flows. Recently, Luo et al. [Philos. Trans. R. Soc. A: Math. Phys. Eng. Sci. 379, 20200397 (2021)] proposed a unified lattice Boltzmann method (ULBM) to integrate the widely used lattice Boltzmann collision operators into a unified framework. In this study, we incorporate additional features into this ULBM in order to simulate multiphase flow under realistic conditions. A nonorthogonal moment set [Fei et al., Phys. Rev. E 97, 053309 (2018)] and the entropic-multi-relaxation-time (KBC) lattice Boltzmann model are used to construct the collision operator. An extended combined pseudopotential model is proposed to realize multiphase flow simulation at high-density ratio with tunable surface tension over a wide range. The numerical results indicate that the improved ULBM can significantly decrease the spurious velocities and adjust the surface tension without appreciably changing the density ratio. The ULBM is validated through reproducing various droplet dynamics experiments, such as binary droplet collision and droplet impingement on superhydrophobic surfaces. Finally, the extended ULBM is applied to complex droplet dynamics, including droplet pancake bouncing and droplet splashing. The maximum Weber number and Reynolds number in the simulation reach 800 and 7200, respectively, at a density ratio of 1000. The study demonstrates the generality and versatility of ULBM for incorporating schemes to tackle challenging multiphase problems

Pore-scale fluid flow simulation coupling lattice Boltzmann method and pore network model

The lattice Boltzmann method and pore network model are two types of the most popular pore-scale fluid flow simulation methods. As a direct numerical simulation method, lattice Boltzmann method simulates fluid flow directly in the realistic porous structures, characterized by high computational accuracy but low efficiency. On the contrary, pore network model simulates fluid flow in simplified regular pore networks of the real porous media, which is more computationally efficient, but fails to capture the detailed pore structures and flow processes. In past few years, significant efforts have been devoted to couple lattice Boltzmann method and pore network model to simulate fluid flow in porous media, aiming to combine the accuracy of lattice Boltzmann method and efficiency of pore network model. In this mini-review, the recent advances in pore-scale fluid flow simulation methods coupling lattice Boltzmann method and pore network model are summarized, in terms of single-phase flow, quasi-static two-phase drainage flow and dynamic two-phase flow in porous media, demonstrating that coupling the lattice Boltzmann method and pore network model offers a promising and effective approach for addressing the up-scaling problem of flow in porous media.Cited as: Zhao, J., Liu, Y., Qin, F., Fei, L. Pore-scale fluid flow simulation coupling lattice Boltzmann method and pore network model. Capillarity, 2023, 7(3): 41-46. https://doi.org/10.46690/capi.2023.06.0

On the flow of soft suspensions through orifices

The behavior of confined suspensions of soft droplets under pressure-driven flow, passing an obstacle within a planar channel, is investigated by means of a mesoscopic lattice Boltzmann model capable of simulating soft non-coalescing droplets. The simulations reveal that the threshold of the pore size, below which the flux vanishes, is between 1 and 2 droplet diameters, and increases with the packing fraction. Moreover, we show that the classical Beverloo relation between the total flux and the pore size is not suitable for the soft suspensions considered here