标题： 一种移位边界法用于热流体流动 显示英文标题

标题： A Shifted Boundary Method for Thermal Flows

摘要： 本文提出了一种不完整八叉树网格实现的移位边界法（Octree-SBM），用于耦合流动与传热的多物理场模拟。具体而言，采用半隐式形式的热纳维叶-斯托克斯方程，在保证精度的同时加速了模拟过程。SBM 能够在截断（拦截）单元上精确施加场和导数边界条件，从而在使用非边界拟合网格时，能够准确计算复杂几何附近的通量。Dirichlet 和 Neumann 边界条件均已在 SBM 框架内实现，结果显示，SBM 可确保基于八叉树网格的 Neumann 边界条件的精确实施。我们通过模拟跨越不同雷诺数（$Re \sim 10^0$--$10^4$）和瑞利数（$Ra \sim 10^3$--$10^9$）范围几个数量级的流体流动现象来展示该方法，涵盖层流、过渡流和湍流流动状态。除了基于残差的变多尺度格式（RB-VMS）外，无需任何额外的数值处理即可准确捕捉这些流动状态下耦合的热流现象及其统计特性。这种方法为计算多物理场模拟中的复杂几何形状、边界条件和流动状态提供了一种可靠且高效的解决方案。 显示英文摘要

摘要： This paper presents an incomplete Octree mesh implementation of the Shifted Boundary Method (Octree-SBM) for multiphysics simulations of coupled flow and heat transfer. Specifically, a semi-implicit formulation of the thermal Navier-Stokes equations is used to accelerate the simulations while maintaining accuracy. The SBM enables precise enforcement of field and derivative boundary conditions on cut (intercepted) elements, allowing for accurate flux calculations near complex geometries, when using non-boundary fitted meshes. Both Dirichlet and Neumann boundary conditions are implemented within the SBM framework, with results demonstrating that the SBM ensures precise enforcement of Neumann boundary conditions on Octree-based meshes. We illustrate this approach by simulating flows across different regimes, spanning several orders of magnitude in both the Rayleigh number ($Ra \sim 10^3$--$10^9$) and the Reynolds number ($Re \sim 10^0$--$10^4$), and covering the laminar, transitional, and turbulent flow regimes. Coupled thermal-flow phenomena and their statistics across all these regimes are accurately captured without any additional numerical treatments, beyond a Residual-based Variational Multiscale formulation (RB-VMS). This approach offers a reliable and efficient solution for complex geometries, boundary conditions and flow regimes in computational multiphysics simulations.