Title: A semi-implicit numerical scheme based on moving Voronoi cells
Abstract
In this talk, I will explain how moving Voronoi grids can be used in computational fluid dynamics. Following the papers of Bruno Després [1] and Volker Springel [2], we pursue a method for compressible Navier-Stokes equations that is as close to being Lagrangian as possible (cells moving with the flow) while combating the undesirable clustering of the Voronoi generating seeds.
Our novel Semi-Implicit Lagrangian Voronoi Approximation (SILVA) can be understood as a particle method, where the Voronoi mesh is a supplementary structure for constructing derivative approximations. Our novelty is a semi-implicit time-marching scheme, allowing larger time steps and thus reducing the frequency of (relatively costly) mesh regeneration. Compared to Smoothed Particle Hydrodynamics (SPH), we obtain smaller stencils and a more efficient wall implementation.
At the end of the talk, I will discuss current obstacles and open questions and try to convince the audience that moving Voronoi schemes have a great potential for solving complex problems, like multiphase modeling and fluid-structure interaction.
References
[1] Bruno Després. Lagrangian Voronoi meshes and particle dynamics with shocks. Computer Methods in Applied Mechanics and Engineering, 418:116427, 2024.
[2] Volker Springel. Hydrodynamic simulations on a moving Voronoi mesh. arXiv preprint arXiv:1109.2218, 2011.
