A Unified Wall-Boundary Condition for the Lattice Boltzmann Method and its Application to Force Evaluation

2014 ◽  
Vol 31 (1) ◽  
pp. 55-68 ◽  
Author(s):  
S.-Y. Lin ◽  
Y.-H. Chin ◽  
F.-L. Yang ◽  
J.-F. Lin ◽  
J.-J. Hu ◽  
...  
Keyword(s):  
Boundary Condition ◽  
Lattice Boltzmann Method ◽  
Lattice Boltzmann ◽  
Solid Wall ◽  
Immersed Boundary ◽  
Equilibrium Pressure ◽  
Good Convergence ◽  
Wall Boundary Condition ◽  
Wall Boundary ◽  
Boltzmann Method

AbstractA unified wall-boundary condition for the pressure-based lattice Boltzmann method (LBM) is proposed. The present approach is developed from the direct-forcing technique in the immersed boundary method and is derived from the equilibrium pressure distribution function. The proposed method can handle many kinds of wall boundaries, such as fixed wall and moving wall boundaries, in the same way. It is found that the new method has the following advantages: (1) simple in concept and easy to implement, (2) higher-order accuracy, (3) mass conservation, and (4) a stable and good convergence rate. Based on this wall-boundary condition, if a solid wall is immersed in a fluid, then by applying Gauss's theorem, the formulas for computing the force and torque acting on the solid wall from fluid flow are derived from the volume integrals over the solid volume instead of from the surface integrals over the solid surface. Based on the pressure-based LBM, inlet and outlet boundary conditions are also proposed. The order of accuracy of the proposed boundary condition is demonstrated with the errors of the velocity field, wall stress, and gradients of velocity and pressure. The steady flow past a circular cylinder is simulated to demonstrate the efficiency and capabilities of the proposed unified method.

A Lattice Boltzmann Method Based Numerical Scheme for Microchannel Flows

2009 ◽  
Vol 131 (8) ◽  
Author(s):  
S. C. Fu ◽  
W. W. F. Leung ◽  
R. M. C. So
Keyword(s):  
Boundary Condition ◽  
Lattice Boltzmann Method ◽  
Lattice Boltzmann ◽  
Numerical Scheme ◽  
Fluid Viscosity ◽  
Two Dimensional ◽  
Wall Boundary Condition ◽  
Wall Boundary ◽  
Microchannel Flows ◽  
Boltzmann Method

Conventional lattice Boltzmann method (LBM) is hyperbolic and can be solved locally, explicitly, and efficiently on parallel computers. The LBM has been applied to different types of complex flows with varying degrees of success, and with increased attention focusing on microscale flows now. Due to its small scale, microchannel flows exhibit many interesting phenomena that are not observed in their macroscale counterpart. It is known that the Navier–Stokes equations can still be used to treat microchannel flows if a slip-wall boundary condition is assumed. The setting of boundary conditions in the conventional LBM has been a difficult task, and reliable boundary setting methods are limited. This paper reports on the development of a finite difference LBM (FDLBM) based numerical scheme suitable for microchannel flows to solve the modeled Boltzmann equation using a splitting technique that allows convenient application of a slip-wall boundary condition. Moreover, the fluid viscosity is accounted for as an additional term in the equilibrium particle distribution function, which offers the ability to simulate both Newtonian and non-Newtonian fluids. A two-dimensional nine-velocity lattice model is developed for the numerical simulation. Validation of the FDLBM is carried out against microchannel and microtube flows, a driven cavity flow, and a two-dimensional sudden expansion flow. Excellent agreement is obtained between numerical calculations and analytical solutions of these flows.

SIMULATION OF FLOW PAST A CIRCULAR CYLINDER USING ENTROPIC LATTICE BOLTZMANN METHOD

2013 ◽  
Vol 25 (01) ◽  
pp. 1340024 ◽  
Author(s):  
CHUAN GU ◽  
SHYAM S. CHIKATAMARLA ◽  
ILIYA V. KARLIN
Keyword(s):  
Boundary Condition ◽  
Circular Cylinder ◽  
Lattice Boltzmann Method ◽  
Lattice Boltzmann ◽  
Three Dimensional ◽  
Wall Boundary Condition ◽  
Flow Past ◽  
Wall Boundary ◽  
Stability And Accuracy ◽  
Boltzmann Method

The entropic lattice Boltzmann method (ELBM) has been demonstrated to bring unconditional stability and accuracy to sub-gird flow simulations. However, the application of ELBM to engineering flows were restricted so far due to the lack of a matching wall boundary condition that retains the accuracy of the method for both resolved and under-resolved simulations. To this end, we show that the recently proposed wall boundary condition for ELBM is reliable and accurate for both these regimes. Three-dimensional (3D) flow past a circular cylinder is taken as a benchmark to show that ELBM is both stable and accurate for range of Reynolds numbers and grid sizes. Several key parameter of this flow are studied in detail.

A Lattice Boltzmann Method Based Numerical Scheme for Microchannel Flows

2008 ◽  
Author(s):  
S. C. Fu ◽  
W. W. F. Leung ◽  
R. M. C. So
Keyword(s):  
Boundary Condition ◽  
Lattice Boltzmann Method ◽  
Lattice Boltzmann ◽  
Numerical Scheme ◽  
Channel Flows ◽  
Fluid Viscosity ◽  
Micro Channel ◽  
Wall Boundary Condition ◽  
Wall Boundary ◽  
Boltzmann Method

Lattice Boltzmann method (LBM) has been recently developed into an alternative and promising numerical scheme for modeling fluid physics and fluid flows. The equation is hyperbolic and can be solved locally, explicitly, and efficiently on parallel computers. LBM has been applied to different types of complex flows with varying degree of success, but rarely to micro-scale flow. Due to its small scale, micro-channel flow exhibits many interesting phenomena that are not observed in its macro-scale counterpart. It is known that the Navier-Stokes equations can still be used to treat micro-channel flows if a slip wall boundary condition is assumed. The setting of boundary conditions in LBM has been a difficult task, and reliable boundary setting methods are limited. This paper reports on the development of an algorithm to solve the Boltzmann equation with a splitting method that allows the application of a slip wall boundary condition. Moreover, the fluid viscosity is accounted for as an additional term in the equilibrium particle distribution function, which offers the ability to simulate both Newtonian and non-Newtonian fluids. An LBM based numerical scheme, which is suitable for micro-channel flows, is proposed. A two-dimensional nine-velocity lattice model is developed for the numerical simulation. Validation of the numerical scheme is carried out against micro-channel, micro-tube and driven cavity flows, and excellent agreement is obtained between numerical calculations and analytical solutions of these flows.

Contact Line Dynamics in Liquid-Vapor Flows Using Lattice Boltzmann Method

2006 ◽  
Author(s):  
Shi-Ming Li ◽  
Danesh K. Tafti
Keyword(s):  
Boundary Condition ◽  
Lattice Boltzmann Method ◽  
Contact Line ◽  
Lattice Boltzmann ◽  
Solid Wall ◽  
Hydrodynamic Theory ◽  
Moving Contact Line ◽  
Moving Contact ◽  
Boltzmann Method ◽  
Contact Line Dynamics

A mean-field free-energy lattice Boltzmann method (LBM) is applied to simulate moving contact line dynamics. It is found that the common bounceback boundary condition leads to an unphysical velocity at the solid wall in the presence of surface forces. The magnitude of the unphysical velocity is shown proportional to the local force term. The velocity-pressure boundary condition is generalized to solve the problem of the unphysical velocity. The simulation results are compared with three different theories for moving contact lines, including a hydrodynamic theory, a molecular kinetic theory, and a linear cosine law of moving contact angle versus capillary number. It is shown that the current LBM can be used to replace the three theories in handling moving contact line problems.

A Boundary Condition-Implemented Immersed Boundary-Lattice Boltzmann Method and Its Application for Simulation of Flows Around a Circular Cylinder

2014 ◽  
Vol 6 (06) ◽  
pp. 811-829 ◽  
Author(s):  
X. Wang ◽  
C. Shu ◽  
J. Wu ◽  
L. M. Yang
Keyword(s):  
Boundary Condition ◽  
Circular Cylinder ◽  
Lattice Boltzmann Method ◽  
Lattice Boltzmann ◽  
Delta Function ◽  
Slip Boundary Condition ◽  
Immersed Boundary ◽  
First Order ◽  
Slip Boundary ◽  
Boltzmann Method

AbstractA boundary condition-implemented immersed boundary-lattice Boltzmann method (IB-LBM) is presented in this work. The present approach is an improvement to the conventional IB-LBM. In the conventional IB-LBM, the no-slip boundary condition is only approximately satisfied. As a result, there is flow penetration to the solid boundary. Another drawback of conventional IB-LBM is the use of Dirac delta function interpolation, which only has the first order of accuracy. In this work, the no-slip boundary condition is directly implemented, and used to correct the velocity at two adjacent mesh points from both sides of the boundary point. The velocity correction is made through the second-order polynomial interpolation rather than the first-order delta function interpolation. Obviously, the two drawbacks of conventional IB-LBM are removed in the present study. Another important contribution of this paper is to present a simple way to compute the hydrodynamic forces on the boundary from Newton’s second law. To validate the proposed method, the two-dimensional vortex decaying problem and incompressible flow over a circular cylinder are simulated. As shown in the present results, the flow penetration problem is eliminated, and the obtained results compare very well with available data in the literature.

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