Multiscale flow simulations using grids and particles
What is the most effective way to simulate fluid flows ? Researchers often separate themselves on the camps of grid based and meshless/particle methods. Particles provide a seamless computational framework to address problems from the atomistic (via Molecular Dynamics) to the continuum description of fluid flows using Navier Stokes equations. Particles, often coupled with Lagrangian descriptions for the Navier Stokes equations, as in vortex methods and Smoothed Particle Hydrodynamics (SPH), provide automatic adaptivity and arguably a minimal number of computational elements. Grid based methods, on the other hand, often associated with Eulerian descriptions, are known to exhibit higher accuracy. We argue that we can get the best of both worlds by suitably coupling particle and grid based methods via remeshing. In remeshed for vortex methods and SPH the particles handle the convective part of the flow field. When the flow map distorts the particle locations we map particle properties onto grid nodes the particles on grids to ensure the convergence and accuracy of the methods. The grid nodes then become the new particles in the following iteration.This hybrid approach has several advantages. The regularity of the data structures associated with Eulerian grids enables efficient solutions of the diffusion and and the Poisson equation. Even more they enable multiresolution simulations, by using wavelet adapted grids to further economize on the number of computational elements. Finally the interplay of grids and particles can be exploited to construct effective multiscale algorithms for flow simulations. I will present examples of this approach in areas ranging from nanofluidics to the largest ever simulations performed in CFD using 13 Trillion elements performing at 14 PFlops to simulate cavitation.