标题： 基于八叉树的移动边界方法用于复杂几何中线性化纳维-斯托克斯方程的多物理场模拟 显示英文标题

标题： Octree-Based Shifted Boundary Method for Multiphysics Simulations Using Linearized Navier-Stokes in Complex Geometries

摘要： 本文介绍了迁移边界方法（SBM）在热流模拟中的应用，利用不完整的八叉树网格（Octree-SBM）进行耦合流动和传热的多物理场模拟。 通过采用纳维-斯托克斯方程的线性化形式，我们在保持精度的同时加速了模拟。 SBM能够在截断的单元上精确施加场和导数边界条件，当使用非边界拟合网格时，允许在复杂几何附近进行精确的通量计算。 在SBM框架内实现了狄利克雷和诺伊曼边界条件，结果表明SBM确保在基于八叉树的网格上精确施加诺伊曼边界条件。 我们通过模拟不同工况下的流动来说明这种方法，在雷诺数（$Ra \sim 10^3$到$10^9$）和雷诺数（$Re \sim 10^0$到$10^4$）变化几个数量级的情况下进行基准测试，覆盖层流、过渡流和湍流工况。 耦合的热流现象以及所有这些工况下的总结统计信息均被准确捕捉，除了基于残差的变分多尺度公式（RB-VMS）外，无需任何额外的数值处理。 这种方法为计算多物理场模拟中的复杂几何结构、边界条件和流动工况提供了一种可靠且高效解决方案。 显示英文摘要

摘要： This paper presents the application of the Shifted Boundary Method (SBM) to thermal flow simulations, utilizing incomplete octree meshes (Octree-SBM) to perform multiphysics simulations that couple flow and heat transfer. By employing a linearized form of the Navier-Stokes equations, we accelerate the simulations while maintaining accuracy. SBM enables precise enforcement of field and derivative boundary conditions on 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 SBM ensures precise enforcement of Neumann boundary conditions on octree-based meshes. We illustrate this approach by simulating flows across different regimes, benchmarking results over several orders of magnitude variation in Rayleigh numbers ($Ra \sim 10^3$ to $10^9$) and Reynolds numbers ($Re \sim 10^0$ to $10^4$), covering laminar, transitional, and turbulent regimes. Coupled thermal-flow phenomena as well as summary 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.