Two new approaches for applying Neumann boundary condition in thermal lattice Boltzmann method

2020 ◽  
Vol 198 ◽  
pp. 104407
Author(s):  
Ali Alipour Lalami ◽  
Ali Hassani Espili
Keyword(s):  
Boundary Condition ◽  
Lattice Boltzmann Method ◽  
Lattice Boltzmann ◽  
Neumann Boundary Condition ◽  
Neumann Boundary ◽  
New Approaches ◽  
Boltzmann Method ◽  
Thermal Lattice Boltzmann

Numerical simulation of Neumann boundary condition in the thermal lattice Boltzmann model

2014 ◽  
Vol 25 (08) ◽  
pp. 1450027 ◽  
Author(s):  
Q. Chen ◽  
X. B. Zhang ◽  
J. F. Zhang
Keyword(s):  
Boundary Condition ◽  
Finite Difference ◽  
Lattice Boltzmann ◽  
Neumann Boundary Condition ◽  
Neumann Boundary ◽  
Extrapolation Method ◽  
Lattice Boltzmann Model ◽  
Boundary Method ◽  
Thermal Lattice Boltzmann ◽  
Boltzmann Model

In this paper, a bilinear interpolation finite-difference scheme is proposed to handle the Neumann boundary condition with nonequilibrium extrapolation method in the thermal lattice Boltzmann model. The temperature value at the boundary point is obtained by the finite-difference approximation, and then used to determine the wall temperature via an extrapolation. Our method can deal with the boundaries with complex geometries, motions and gradient boundary conditions. Several simulations are performed to examine the capacity of this proposed boundary method. The numerical results agree well with the analytical solutions. When compared with a representative boundary method, an improved performance is observed. The results also show that the proposed scheme together with nonequilibrium extrapolation method has second-order accuracy.

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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