New trends in Multi-Scale Simulation using Hybrid Grid-Particle Vortex Methods
Résumé
The purpose of this talk is to present a multi-scale Vortex-in-Cell method, for direct numerical simulation of three dimensional fluid flows. Vortex methods are Lagrangian. They are among the most challenging particle method, and have been dramatically improved during the last decade. This talk will present the main ideas of these methods, implemented in the open source package COMMA, funded by ANR and based on high performance packages FISHPACK and AGRIF. Among numerical methods aiming at solving the equations of fluid dynamics, the particle methods are renowned for their ability to compute accurately transport and convective effects. Most of the current challenges focus on the Navier-Stokes equations and their generalizations : multi-fluids, reactive flows, combustion, complex boundary conditions. In this short communication , one focuses on the basic three-dimensional Navier-Stokes equations, for an incompress-ible fluid, given by ∂u ∂t + u · u − ν∆u = f ρ − p ρ (1) where u is the divergence-free velocity field satisfying the no-slip condition u = 0 on Γ, p the pressure, ρ the density, ν the kinematic viscosity, and f the external force. For an incompressible fluid of constant density and viscosity, taking the curl of equation (1) and introducing the vorticity as ω = curlu, leads to ∂ω ∂t + u · ω − ω · u − ν∆ω = 0 (2) with kinematic no-slip boundary conditions u = 0, for external forces deriving from a potential (ie is the gradient of a scalar function).
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