Abstract
We have tested the accuracy and stability of lattice-Boltzmann (LB) simulations of the convection-diffusion equation in a two-dimensional channel flow with reactive-flux boundary conditions. We compared several different implementations of a zero-concentration boundary condition using the Two-Relaxation-Time (TRT) LB model. We found that simulations using an interpolation of the equilibrium distribution were more stable than those based on Multi-Reflection (MR) boundary conditions. We have extended the interpolation method to include mixed boundary conditions, and tested the accuracy and stability of the simulations over a range of Damköhler and Péclet numbers.
Highlights
The lattice Boltzmann method (LBM) has been used primarily to solve fluid dynamics problems [1,2,3,4], but it can be used to approximate solutions of the convection-diffusion equation for a scalar field C [5],∂t C + u · ∇C = D ∇2 C. (1)In this paper we envisage C as describing a reactant concentration that is sufficiently dilute that it does not affect the flow, but advects and diffuses as a passive scalar in a predetermined velocity field u
Since the equilibrium distribution can be determined at the solid-fluid boundary, there is an additional node for interpolation, so that only a single fluid node is required as in the case of the bounce-back rule itself
We have proposed a non-equilibrium extrapolation method in TRT model for simulating convection-diffusion flow with a reactive boundary condition
Summary
The lattice Boltzmann method (LBM) has been used primarily to solve fluid dynamics problems [1,2,3,4], but it can be used to approximate solutions of the convection-diffusion equation for a scalar field C [5],. Since the equilibrium distribution can be determined at the solid-fluid boundary, there is an additional node for interpolation, so that only a single fluid node is required as in the case of the bounce-back rule itself This idea underpins several different improvements to the bounce-back rule [21,22,23]; in this paper we focus on the first implementation [21], which proves to be the most stable. The non-equilibrium extrapolation method for the convection is proposed for the Dirichlet or mixed boundary conditions in Sections 3 and 4. This method combined with finite difference method is easy to implement and can be used for stationary and moving boundary.
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