Journal
COMPUTERS & MATHEMATICS WITH APPLICATIONS
Volume 59, Issue 7, Pages 2178-2193Publisher
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.camwa.2009.08.043
Keywords
Thermal boundary conditions; Thermal lattice Boltzmann simulations; Macroscopic energy equation; Wall; Corner
Categories
Funding
- Taiwan National Science Council [94-2212-E-007-059]
Ask authors/readers for more resources
Consistent 2D and 3D thermal boundary conditions for thermal lattice Boltzmann simulations are proposed. The boundary unknown energy distribution functions are made functions of known energy distribution functions and correctors, where the correctors at the boundary nodes are obtained directly from the definition of internal energy density. This boundary condition can be easily implemented on the wall and corner boundary using the same formulation. The discrete macroscopic energy equation is also derived for a steady and fully developed channel flow to assess the effect of the boundary condition on the solutions, where the resulting second order accurate central difference equation predicts continuous energy distribution across the boundary, provided the boundary unknown energy distribution functions satisfy the macroscopic energy level. Four different local known energy distribution functions are experimented with to assess both this observation and the applicability of the present formulation, and are scrutinized by calculating the 2D thermal Poiseuille flow, thermal Couette flow, thermal Couette flow with wall injection, natural convection in a square cavity, and 3D thermal Poiseuille flow in a square duct. Numerical simulations indicate that the present formulation is second order accurate and the difference of adopting different local known energy distribution functions is, as expected, negligible, which are consistent with the results from the derived discrete macroscopic energy equation. (C) 2009 Elsevier Ltd. All rights reserved.
Authors
I am an author on this paper
Click your name to claim this paper and add it to your profile.
Reviews
Recommended
No Data Available