Hydrostatic equilibrium is a static state that the fluid pressure is balanced with gravity. Classic finite difference and finite volume methods cannot maintain this equilibrium state on discrete scales, and produce non-physical phenomena often such as spurious currents. In this work, volume integral of the source term is implemented at cell interface, so that the balance of pressure and gravity under discrete conditions is achieved on discrete scales. A well-balanced gas kinetic scheme of the Navier-Stokes(NS) equation is therefore constructed. The scheme maintains accurately the static equilibrium state under isothermal conditions and captures small perturbation propagation near equilibrium state at machine precision. At the same time, the scheme solves non-isothermal stratified flow near equilibrium state. Apart from the non-isothermal equilibrium described by Euler's equation, the scheme can also represent balance of thermal conduction in addition to force balance. It is shown that the scheme preserves second-order accuracy with respect to both density and temperature distribution when simulating an non-isothermal equilibrium state. Numerical examples reveal that the scheme is a potential tool in simulating stratified flow of temperature and density under gravitational field.

With lattice Boltzmann method, thermal miscible displacement process in porous media was investigated numerically in pore scale. Influence of thermal viscous diffusion coefficient (β_T) and Lewis number (Le) on interface shape and sweep efficiency are quantitatively analyzed. It shows that with the increase of β_T, the instability of interface increases and the sweep efficiency decreases. As β_T>0, with increase of Le, interface instability decreases; Interface between displacement fluid and displaced fluid tends to be flat; Fingertip residual rate decreases and sweep efficiency increases. As β_T<0, effects of Le on sweep efficiency are opposite.

We extend gas kinetic scheme (GKS) to low-speed porous media flow, and test feasibility and effectiveness of the method. It shows that GKS is second-order accurate in space and is capable of predicting permeability of porous media. Compared with single-relaxation-time lattice Boltzmann method, GKS implements precisely no slip boundary condition, thus reflects correctly characteristics of viscosity-independent permeability. For complex flow in Berea sandstone slice structure, simulation results are in good agreement with experimental data, and permeability is calculated accurately. A criteria of Ma number in GKS is proposed for Darcy flow. It shows that GKS could be a promising scheme for porous media flows.

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.

Using Lattice Boltzmann method on GPU, viscous fingering of chemical fluids in porous media is simulated at pore scale. Influence of chemical reaction on fluid mixing is quantified. A one-variable chemical model admitting two stable states is adopted and a homogeneous artificial medium is generated by Quartet Structure Generation Set (QSGS) method. It shows that chemical reaction makes fingering interfaces sharp, restrains fluid mixing, and causes demixing. Influence is enhanced with increase of chemical reaction rate.

Capture on a vibrating cylinder is simulated. Flow field is obtained with lattice Boltzmann method combined multi-block lattice Boltzmann method. Motion of single particle is calculated with Langevin equation by Lagrange integration. Drag force and Brownian diffusion is considered only. Cylinder does harmonic motion in flow direction with various frequency and amplitude at Re=200. As a result, different flow pattern present. We found capture efficiency raises. Especially at AⅢ vortex pattern, distribution of initial position deviates from center.

Viscous fingering with simultaneous chemical reaction at interface is investigated in a micro channel based on lattice Boltzmann method. One-variable chemical model admitting two stable states is adopted. We focus on influence of chemical reaction on viscous fingering. It is found that fluid interface become thinner with increase of reaction rate, while changes of steady state concentration (interfacial concentration where rate of chemical reactions is zero) influence position and morphology of viscous fingering. Isolated droplet can be formed from tip of finger.

A lattice Boltzmann model for miscible viscous fingering in porous media is proposed. Stable displacement between two fluids with same viscosity is simulated. Good agreement with analytical solution is obtained. Specifically,effects of viscosity contrast and Peclet number are investigated. It shows that great viscosity contrast makes fingers grow faster. As viscosity contrast is given,there exists a critical Peclet number above which tip-splitting happens. Study on transversely averaged concentration profile indicates that mixing length first goes as t^1/2,then shifts into a linear dependence in t.

A sparse lattice representation lattice Boltzmann method algorithm is implemented on Graphics Processing Units (GPU) to accelerate pore scale flow simuation.Prefomance testing shows that sparse lattice representation approach grately reduces memory requirement and maintains performance under low porosity compared with basic algorithm.Overall speedup reaches two orders of magnitude compared with serial code.Various factors including collision model,float number precision,and GPU that affect computing speed of the algorithm are invesgated independently.It indicates that MRT model runs as fast as LBGK model on new generation of GPU cards.While on old GPU cards,MRT model's computing speed matchs LBGK only when using single precision float.

We study carbonation process of CaO with lattice Boltzmann method. Specifically,effects of porosities of CaO particles on carbonation rate are investigated. It shows that efficiency depends on porosity nonlinearly due to competition between molar mass and permeability of particles.

A detailed comparative study is made to investigate three boundary treatment schemes in lattice Bohzmann methods (LBM).They are half-way bounce back scheme,sub-grid scheme,and a scheme to treat curved boundaries.It is found that particle translational and angular velocities calculated with half-way bounce back scheme oscillate strongly,while particle velocities obtained by sub-grid scheme evolve smoothly.

We present an extension of lattice-Boltzmann-lattice-gas method proposed by Masselot and Chopard for gas-solid flows,in which the drag force between gas and solid is considered.The method is applied to particles in a driven cavity flow.Effects of Stokers number and total number of particles are analyzed.Simulation results are compared with previous works.It shows that the proposed LBE-LGA method can serve as a promising tool for simulating gas-particle flows.

In order to describe microscale flows in compact porous media with lattice Boltzmann method,we extend a model proposed by Guo et al designed for micro gas flows in a single channel to porous medium.The extended model is used to simulate two simplified porous structures.Dependence of permeability on Knudsen number and averaged pressure is studied and analyzed theoretically.Simulated results are consistent with experimental results reported.It shows that the lattice Boltzmann method can serve as a promising tool for simulating gas flows through a compact porous medium.