We extend the shifted boundary method (SBM) to the simulation of incompressible fluid flow using immersed octree meshes. Previous work on SBM for fluid flow primarily utilized two- or three-dimensional unstructured tetrahedral grids. Recently, octree grids have become an essential component of immersed CFD solvers, and this work addresses this gap and the associated computational challenges. We leverage an optimal (approximate) surrogate boundary constructed efficiently on incomplete and adaptive octree meshes. The resulting framework enables the simulation of the incompressible Navier-Stokes equations in complex geometries without requiring boundary-fitted grids. Simulations of benchmark tests in two and three dimensions demonstrate that the Octree-SBM framework is a robust, accurate, and efficient approach to simulating fluid dynamics problems with complex geometries.

翻译：本文将移位边界法（SBM）扩展至基于浸入式八叉树网格的不可压缩流体流动模拟。先前针对流体流动的SBM研究主要采用二维或三维非结构化四面体网格。近年来，八叉树网格已成为浸入式计算流体力学求解器的关键组成部分，本研究旨在填补这一空白并应对相关的计算挑战。我们利用在非完整且自适应的八叉树网格上高效构建的最优（近似）代理边界，建立了一个无需边界贴合网格即可模拟复杂几何中不可压缩Navier-Stokes方程的框架。二维与三维基准测试的模拟结果表明，Octree-SBM框架是处理复杂几何流体动力学问题的一种鲁棒、精确且高效的方法。