Numerical Investigation of Moving Boundary Flows Using a Semi-Lagrangian/ALE Framework

Abstract

The numerical simulation of fluid flows involving moving boundaries and high convective flows remains a significant challenge in Computational Fluid Dynamics (CFD). This work presents a numerical study of single-phase flows using a Semi-Lagrangian (SL) method for the treatment of the convective terms, integrated into an Arbitrary Lagrangian-Eulerian (ALE) framework for mesh movement. The SL scheme is employed to circumvent the CourantFriedrichs-Lewy (CFL) stability restrictions typically associated with Eulerian methods [3], allowing for larger time steps without compromising numerical stability. Simultaneously, the ALE formulation provides a flexible coupling between the fluid motion and the deforming domain, ensuring high mesh quality even under significant boundary displacements [2]. The mathematical modeling focuses on the Navier-Stokes equations, where the mesh velocity is explicitly accounted for in the conservation laws [1]. Preliminary results demonstrate that the combination of SL and ALE effectively reduces numerical diffusion in convectiondominated problems [4] while maintaining geometric fidelity. This approach proves to be highly relevant for simulating complex engineering systems, such as fluid-structure interaction (FSI) in offshore components, piston-cylinder assemblies, and cardiovascular hemodynamics. The developed framework offers a computationally efficient alternative for transient simulations where both precision and stability are paramount.