Model-Reduced Variational Fluid Simulation

摘要

compressiblernfluids, which combines the efficiency gains of dimensionrnreduction, the qualitative robustness of coarse spatial andrntemporal resolutions of geometric integrators, and the simplicity ofrnsub-grid accurate boundary conditions on regular grids to deal withrnarbitrarily-shaped domains. At the core of our contributions is arnfunctional map approach to fluid simulation for which scalar- andrnvector-valued eigenfunctions of the Laplacian operator can be easilyrnused as reduced bases. Using a variational integrator in time tornpreserve liveliness and a simple, yet accurate embedding of the fluidrndomain onto a Cartesian grid, our model-reduced fluid simulatorrncan achieve realistic animations in significantly less computationalrntime than full-scale non-dissipative methods but without the numericalrnviscosity from which current reduced methods suffer. We alsorndemonstrate the versatility of our approach by showing how it easilyrnextends to magnetohydrodynamics and turbulence modeling inrn2D, 3D and curved domains.