Abstract In this work we introduce a boundary condition for thermal lattice Boltzmann simulations that contain a Dirichlet boundary condition by bouncing back the non-equilibrium distribution of the energy distribution function. To this end the thermal lattice Boltzmann equation is modified by introducing an additional collision term that takes into account the thermal diffusivity and local solid volume fraction of a lattice (partially) covered by the solid phase. Asymptotic analysis of the boundary condition confirms that it is of second order accuracy. The method is validated using (i) an analytical solution for the Nusselt number correlation of a single sphere in an unbounded stationary fluid and (ii) direct numerical simulations of the heat transfer between a fluid and individual particles.

中文翻译：

---

热晶格 Boltzmann 方法的 Dirichlet 边界条件

摘要 在这项工作中，我们为包含狄利克雷边界条件的热晶格 Boltzmann 模拟引入了一个边界条件，通过反弹能量分布函数的非平衡分布。为此，通过引入额外的碰撞项来修改热晶格 Boltzmann 方程，该碰撞项考虑了被固相覆盖的晶格（部分）的热扩散率和局部固体体积分数。边界条件的渐近分析证实它具有二阶精度。该方法使用 (i) 无界静止流体中单个球体的 Nusselt 数相关性的解析解和 (ii) 流体与单个粒子之间的热传递的直接数值模拟进行验证。