Octree-based adaptive mesh refinement and the shifted boundary method for efficient fluid dynamics simulations

This paper presents an adaptive mesh refinement (AMR) framework integrated with the shifted boundary method (SBM) for incompressible flow and coupled thermal-flow simulations. Our framework leverages octree-based AMR, enabling hierarchical and dynamic mesh refinement driven by vorticity magnitude. This strategy enables capturing complex vorticity structures and steep thermal gradients while significantly reducing computational costs compared to traditional uniform refinement approaches, particularly for flows around complex geometries. The octree-based architecture ensures efficient data management, including robust intergrid transfer and load balancing, which is critical for scalability in distributed-memory environments. Dynamic mesh adaptivity is demonstrated for complex geometries where achieving ideal refinement is often non-trivial due to the irregular boundaries. SBM enhances this adaptability by accurately enforcing boundary conditions on intricate and non-conformal geometries without requiring boundary-fitted meshes. Together, these methods address longstanding challenges in computational fluid dynamics, providing a resource-efficient yet accurate approach for capturing critical flow and thermal features. The utility of the framework is demonstrated through numerical experiments, showcasing its ability to adapt dynamically to evolving flow and thermal patterns in diverse and challenging geometries.