Simulating incompressible flows over complex geometries using the shifted boundary method with incomplete adaptive octree meshes

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.