The power of Nonnegative Matrices in Multi-species Hydrodynamics
Self-consistent multi-species momentum transfer is crucial for the study of a diversity of systems in the field of fluid and particle dynamics. The coupling of the multi-species momentum transfer to the Navier-Stokes equations challenges the stability, complexity, and efficiency of existing numerical methods. However, we have recently developed a numerical scheme that overcomes these challenges for an arbitrary number of species. In this seminar, I will introduce the numerical scheme and summarize its stability and convergence properties derived from the theory of non-singular M-matrices. Then, I will showcase the implementation of the new scheme in the publicly available code FARGO3D and describe how we exploit High-Performance-Computing (HPC) resources with fluid-parallelization combined with GPU computing capability. Finally, I will highlight recent applications in the field of Planet Formation with particular emphasis on how this numerical method correctly describes the aerodynamic coupling between gas and multiple dust species. This novel method opens up new opportunities for investigating several fundamental processes involving dust dynamics which have been so far investigated in the realm of a single dust-species approach.
Password: “arizona” (all lower case)