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Speaker: Leonardo Krapp, University of Concepción
Title: The Power of Nonnegative Matrices in Multi-Species Hydrodynamics
Abstract: Self-consistent momentum transfer between multiple species is essential for understanding a wide range of phenomena in fluid and particle dynamics. Coupling multi-species momentum exchange to the Navier-Stokes equations, however, poses significant challenges to the stability, complexity, and efficiency of conventional numerical methods. We have recently developed a novel numerical scheme that overcomes these obstacles for systems involving an arbitrary number of species. In this seminar, I will present the key features of this scheme and discuss its rigorous stability and convergence properties, which stem from the theory of nonsingular M-matrices (closely related to nonnegative matrix theory). I will then explain how to enhance the method’s accuracy using diagonally implicit Runge-Kutta time integration schemes. Finally, I will showcase recent applications in the field of planet formation, with particular emphasis on the accurate description of aerodynamic coupling between gas and multiple dust species. This capability enables realistic modeling of dust dynamics in protoplanetary disks, going beyond the limitations of traditional single-dust-species approaches. This new method opens exciting opportunities to investigate fundamental processes in multi-species dusty gas dynamics that were previously inaccessible or poorly resolved.