Title: Collocated Simulation of Incompressible Flows on Node-Based Octrees
Abstract:
Incompressible fluid flows are ubiquitous in science and engineering applications and lie at the heart of numerous research questions. Developing control strategies to minimize drag, understanding arterial wall deformation in the human heart, and even optimizing the energy consumption of automotive spray painting operations all require a detailed understanding of incompressible flows. For most of these phenomena, analytical solutions do not exist, and experimental approaches can be difficult and costly to create. Numerical simulations are the natural choice for studying these problems. Still, despite decades of computational advancement, their development remains challenging, especially when irregular geometries, adaptive grids, or complex boundary conditions are involved. For this reason, it is essential to develop high-performance computational fluid dynamics tools that are accessible and straightforward to implement, which can be achieved, for example, by minimizing the number of unique data structures and simplifying data access patterns. This seminar will present a novel collocated projection method for solving the incompressible Navier-Stokes equations with arbitrary boundaries. Our approach employs non-graded octree grids, where all variables are stored at the nodes. To discretize the viscosity and projection steps, we utilize supra-convergent finite difference approximations with sharp boundary treatments. Both the properties and performances of the method will be discussed through theoretical and numerical explorations.
