Lattice Boltzmann Method For Fluids Research Articles

Application of the ghost fluid lattice Boltzmann method to moving curved boundaries with constant temperature or heat flux conditions

In this paper, for the first time, the ghost-fluid lattice Boltzmann method (GF-LBM) is combined with a refilling scheme to simulate the heat transfer from moving bodies with curved boundaries. Two thermal boundary conditions namely, the constant temperature and constant heat flux are considered at the moving curved boundaries. First, the Galilean invariance of the presented method is verified by comparing the results of the problem of heat transfer from a cylinder in a crossflow, in two different inertial references. Next, the sedimentation of a cold particle in a vertical channel is simulated and the results of the presented method are compared to those from the conventional numerical methods, available in the literature, and a good agreement is observed. To sum up, the results of this study showed that the presented GF-LBM with refilling was capable of simulating the thermal moving curved boundaries with excellent accuracy.

New formulation for the simulation of the conjugate heat transfer at the curved interfaces based on the ghost fluid lattice Boltzmann method

ABSTRACTIn the present study, a new method for simulation of the conjugate heat transfer conditions at the curved interface of two media with different thermal properties is proposed based on the ghost fluid lattice Boltzmann method (GF-LBM). The proposed method significantly benefits from the inherent feature of the GF-LBM in availability of the temperature gradient normal to the interface. To test the accuracy of the presented method, three different case studies are simulated. The results revealed the second-order accuracy of the proposed conjugate heat transfer formulation. Furthermore, when compared to the available analytical solutions, the results of this study showed better agreement compared to the results of the other available methods.

Developing a ghost fluid lattice Boltzmann method for simulation of thermal Dirichlet and Neumann conditions at curved boundaries

ABSTRACTIn this paper, a ghost fluid thermal lattice Boltzmann method is developed to simulate Dirichlet and Neumann thermal boundary conditions at curved boundaries. As such, a new formulation for both thermal boundary conditions is developed using a bilinear interpolation method. The presented method is also formulated to address the special cases that arise when the values of the macroscopic variables are interpolated at the image points surrounded by many solid nodes as well as the fluid nodes. The results of the presented method are compared to those available in the literature from conventional numerical methods, and excellent agreement is observed.

A ghost fluid Lattice Boltzmann method for complex geometries

SUMMARYA ghost fluid Lattice Boltzmann method (GF‐LBM) is developed in this study to represent complex boundaries in Lattice Boltzmann simulations of fluid flows. Velocity and density values at the ghost points are extrapolated from the fluid interior and domain boundary via obtaining image points along the boundary normal inside the fluid domain. A general bilinear interpolation algorithm is used to obtain values at image points which are then extrapolated to ghost nodes thus satisfying hydrodynamic boundary conditions. The method ensures no‐penetration and no‐slip conditions at the boundaries. Equilibrium distribution functions at the ghost points are computed using the extrapolated values of the hydrodynamic variables, while non‐equilibrium distribution functions are extrapolated from the interior nodes. The method developed is general, and is capable of prescribing Dirichlet as well as Neumann boundary conditions for pressure and velocity. Consistency and second‐order accuracy of the method are established by running three test problems including cylindrical Couette flow, flow between eccentric rotating cylinders and flow over a cylinder in a confined channel. Copyright © 2011 John Wiley & Sons, Ltd.

Embedding sharp interfaces within the lattice Boltzmann method for fluids with arbitrary density ratios

Current lattice Boltzmann methods for simulating two fluids create a diffuse interface between the fluids. In this work, we develop a novel technique for embedding sharp interfaces between fluids with unbounded density ratios for the LB method. Distribution functions streamed across an interface are transformed so that the receiving node is passed information corresponding to its fluid phase. Two different methods are employed to determine the transformation. The first uses analytical distribution functions from steady Poiseuille flow to determine the jump in moments of the distribution functions across the interface. The second uses approximate expansions of distribution functions to determine jumps in distribution functions. The accuracy and stability of the methods are examined in simulations of Poiseuille-Couette flows with an interface parallel to the walls. Both methods show linear convergence to the analytical solution.

Multicomponent lattice Boltzmann method for fluids with a density contrast

We present and verify a multicomponent lattice Boltzmann simulation scheme for two immiscible and incompressible fluids with a large density contrast. Our method is constructed from a continuum approximation description of a single inhomogeneous, and essentially incompressible, fluid. The equations that arise from this analysis are mapped onto an established multicomponent lattice Boltzmann method. The approach avoids the computational expense of a numerical solution of the fluid pressure field in a separate step. We present results obtained with our model which validate the initial assumptions and verify correct static and dynamic operation of the model up to a fluid density contrast ratio of more than 500. The paper concludes with an example that illustrates the potential utility of the approach by modeling a gas bubble rising under gravity and breaking through a free surface.

Lattice Boltzmann simulations of wetting and its application to disproportionate permeability reducing gel

The binary fluid lattice Boltzmann method is a promising numerical scheme to simulate the flow of two immiscible fluids at the pore level. In particular, the method minimizes an appropriate free energy functional thus ensuring a thermodynamically consistent behaviour in equilibrium. We present an extension of this method, such that walls with different wettability can be included. This is done by adding a “background chemical potential” to the fluid chemical potential. A calibration of the wettability is given, showing how the equilibrium contact angle depends on the background chemical potential. Next, the method is used in a qualitative study of gel-placement in a fractional-wet porous medium model. The presence of gel shows to reduce the water permeability more than the oil permeability. Thus, the wanted disproportionate permeability reduction (DPR) effect applies.