scholarly journals Consistent Wall Boundary Condition for Lattice-Boltzmann Method.

2002 ◽  
Vol 68 (670) ◽  
pp. 1677-1683
Author(s):  
Jun HIOKI ◽  
Takeo KAJISHIMA
Keyword(s):  
Boundary Condition ◽  
Lattice Boltzmann Method ◽  
Lattice Boltzmann ◽  
Wall Boundary Condition ◽  
Wall Boundary ◽  
Boltzmann 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.

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.

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.

scholarly journals Involving the Navier–Stokes equations in the derivation of boundary conditions for the lattice Boltzmann method

2011 ◽  
Vol 369 (1944) ◽  
pp. 2184-2192 ◽  
Author(s):  
Joris C. G. Verschaeve
Keyword(s):  
Boundary Condition ◽  
Lattice Boltzmann Method ◽  
Lattice Boltzmann ◽  
Stokes Equations ◽  
Slip Boundary Condition ◽  
Navier Stokes ◽  
Grid Spacing ◽  
Navier Stokes Equations ◽  
Slip Boundary ◽  
Boltzmann Method

By means of the continuity equation of the incompressible Navier–Stokes equations, additional physical arguments for the derivation of a formulation of the no-slip boundary condition for the lattice Boltzmann method for straight walls at rest are obtained. This leads to a boundary condition that is second-order accurate with respect to the grid spacing and conserves mass. In addition, the boundary condition is stable for relaxation frequencies close to two.

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