A joint absorbing boundary for the multiple-relaxation-time lattice Boltzmann method in seismic acoustic wavefield modeling

Conventional seismic wave forward simulation generally uses mathematical means to solve the macroscopic wave equation,and then obtains the corresponding seismic wavefield.Usually,when the subsurface structure is finely constructed and the continuity of media is poor,this strategy is difficult to meet the requirements of accurate wavefield calculation.This paper uses the multiple-relaxation-time lattice Boltzmann method(MRT-LBM)to conduct the seismic acoustic wavefield simulation and verify its computational accuracy.To cope with the problem of severe reflections at the truncated boundaries,we analogize the viscous absorbing boundary and perfectly matched layer(PML)absorbing boundary based on the single-relaxation-time lattice Boltzmann(SRT-LB)equation to the MRT-LB equation,and further,propose a joint absorbing boundary through comparative analysis.We give the specific forms of the modified MRT-LB equation loaded with the joint absorbing boundary in the two-dimensional(2D)and three-dimensional(3D)cases,respectively.Then,we verify the effects of this absorbing boundary scheme on a 2D homogeneous model,2D modified British Petroleum(BP)gas-cloud model,and 3D homogeneous model,respectively.The results reveal that by comparing with the viscous absorbing boundary and PML absorbing boundary,the joint absorbing boundary has the best absorption performance,although it is a little bit complicated.Therefore,this joint absorbing boundary better solves the problem of truncated boundary reflections of MRT-LBM in simulating seismic acoustic wavefields,which is pivotal to its wide application in the field of exploration seismology.

Cavitation Bubble Collapse near a Curved Wall by the Multiple-Relaxation-Time Shan-Chen Lattice Boltzmann Model

The cavitation bubble collapse near a cell can cause damage to the cell wall. This effect has received increasing attention in biomedical supersonics. Based on the lattice Boltzmann method, a multiple-relaxation-time Shan–Chen model is built to study the cavitation bubble collapse. Using this model, the cavitation phenomena induced by density perturbation are simulated to obtain the coexistence densities at certain temperature and to demonstrate the Young–Laplace equation. Then, the cavitation bubble collapse near a curved rigid wall and the consequent high-speed jet towards the wall are simulated. Moreover, the influences of initial pressure difference and bubble-wall distance on the cavitation bubble collapse are investigated.

Two-dimensional Multiple-Relaxation-Time Lattice Boltzmann model for compressible and incompressible flows

In the paper we extend the Multiple-Relaxation-Time （MRT） Lattice Boltzmann （LB） model pro- posed in [Europhys. Lctt., 2010, 90： 54003] so that it is suitable also for incompressible flows. To decrease tile artificial oscillations, the convection term is discretized by the flux linfiter scheme with splitting technique. A new model is validated by some well-known benchmark tests, including Rie- mann problem and Couette flow, and satisfying agreements are obtained between the sinmlation results and ana.lytical ones. In order to show the merit of LB model over traditional methods, the non-equilibrium characteristics of system are solved. The simulation results are consistent with the physical analysis.

Improving the Stability of theMultiple-Relaxation-Time Lattice Boltzmann Method by a Viscosity Counteracting Approach

Numerical instability may occur when simulating high Reynolds number flows by the lattice Boltzmann method(LBM).The multiple-relaxation-time(MRT)model of the LBM can improve the accuracy and stability,but is still subject to numerical instability when simulating flows with large single-grid Reynolds number(Reynolds number/grid number).The viscosity counteracting approach proposed recently is a method of enhancing the stability of the LBM.However,its effectiveness was only verified in the single-relaxation-time model of the LBM(SRT-LBM).This paper aims to propose the viscosity counteracting approach for the multiple-relaxationtime model(MRT-LBM)and analyze its numerical characteristics.The verification is conducted by simulating some benchmark cases:the two-dimensional(2D)lid-driven cavity flow,Poiseuille flow,Taylor-Green vortex flow and Couette flow,and threedimensional(3D)rectangular jet.Qualitative and Quantitative comparisons show that the viscosity counteracting approach for the MRT-LBMhas better accuracy and stability than that for the SRT-LBM.

Investigation of mass transfer model of CO_(2) absorption with Rayleigh convection using multi-relaxation time lattice Boltzmann method

CO_(2) absorption into absorbents is a widely used method to reduce carbon emissions,in which the concentration gradient near the gas-liquid interface may induce Rayleigh convection(RC).Once RC occurs,the mass transfer rate will be significantly enhanced.Therefore,it is necessary to explore the mass transfer enhancement mechanism further and develop a penetration/surface divergence hybrid mass transfer model.In this study,we conduct research on the process of CO_(2) absorption into ethanol with RC.Firstly,we use a multi-relaxation time lattice Boltzmann method to simulate the absorption process and obtain the flow and concentration fields.And we also verify the reliability of the numerical simulation results by comparing with the experimental results.Then,we analyze the characteristics of non-uniform flow and concentration fields in RC.Moreover,we divide the near-interface region into diffusion-dominated and convection-dominated mass transfer zones by checking whether the horizontal average velocity is greater than 1.0×10^(-4) m·s^(-1).Furthermore,based on the differences in mass transfer mechanisms of the aforementioned two zones,we propose a penetration/surface divergence hybrid model to predict the instantaneous mass transfer coefficient.The prediction results demonstrate that the hybrid model can precisely predict the instantaneous mass transfer coefficient of the entire CO_(2) absorption process.Our proposed hybrid model provides a promising way to deal with the complex mass transfer problems with non-uniform flow and concentration fields.

Prandtl number effects in MRT lattice Boltzmann models for shocked and unshocked compressible fluids

This paper constructs a new multiple relaxation time lattice Boltzmann model which is not only for the shocked compressible fluids,but also for the unshocked compressible fluids.To make the model work for unshocked compressible fluids,a key step is to modify the collision operators of energy flux so that the viscous coefficient in momentum equation is consistent with that in energy equation even in the unshocked system.The unnecessity of the modification for systems under strong shock is analyzed.The model is validated by some well-known benchmark tests,including thermal Couette flow,Riemann problem.The first system is unshocked and the latter is shocked.In both systems,the Prandtl number effects are checked.Satisfying agreements are obtained between new model results and analytical ones.

Viscosity, heat conductivity, and Prandtl number effects in the Rayleigh-Taylor Instability

The two-dimensional Rayleigh-Taylor instability problem is simulated with a multiple-relaxation-time discrete Boltzmann model with a gravity term. Viscosity, heat conductivity, and Prandtl number effects are probed from macroscopic and nonequilibrium viewpoints. In the macro sense, both viscosity and heat conduction show a significant inhibitory effect in the reacceleration stage, which is mainly achieved by inhibiting the development of the Kelvin-Helmholtz instability. Before this, the Prandtl number effect is not sensitive. Viscosity, heat conductivity, and Prandtl number effects on nonequilibrium manifestations and the degree of correlation between the nonuniformity and the nonequilibrium strength in the complex flow are systematically investigated.

Entropy Generation Analysis around Airfoil using Multi-Block Lattice Boltzmann Method

This present paper proposes aerodynamic forces and entropy generation characteristics on theflow past two-dimensional airfoil at low Reynolds number by multiple-relaxation-time lattice Boltzmann method to clarify theflow loss mechanism.The block mesh refinement was adopted in which a higher accuracy was needed in parts of the domain characterized by complexflow.The interpolated bounce-back method was used to treat the irregular curve.This numerical method can effectively solve the complexflowfield simulation problems with reasonable accuracy and reli-ability by simulatingflow around plate and airfoil.Based on second law of thermo-dynamics,an expression of entropy generation rate for arbitrary control volume was derived theoretically which could accurately quantify the local irreversible loss of theflowfield at any position.After that,a comprehensive numerical study was conducted to analyze relationship of entropy generation and drag force by taking NACA0012 air-foil as the research object.For unsteady condition,entropy generation rate and the drag force are not linearly related any more.Losses due to steady effects mainly con-sider the irreversibility in the boundary layer and wake while the unsteady effects come from the interaction between the main separation vortex and the trailing shed-ding vortex.