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Abstract

We propose several advances in the simulation of fluids for computer graphics. We concentrate on particle-in-cell methods and related sub-problems. We develop high-order accurate extensions to particle-in-cell methods demonstrated on a variety of equations, including constrained dynamics with implicit-explicit time integration. We track the liquid-air interface with an explicit mesh, which we show how to do in a provably exact fashion. To address the mismatched simulation and surface resolution, we solve the partial differential equations in each time step with with a p-adaptive discontinuous Galerkin discretization. This allows us to use a coarse regular grid for the entire simulation. For solving the resulting linear system, we propose a novel mostly-algebraic domain decomposition preconditioner that automatically creates a coarse discontinuous Galerkin approximation of the problem.