DOI Bookmark: http://doi.ieeecomputersociety.org/10.1109/TVCG.2013.105
Markus Ihmsen , University of Freiburg, Freiburg
Jens Cornelis , University of Freiburg, Freiburg
Barbara Solenthaler , ETH Zürich, Zürich
Christopher Horvath , Pixar Animation Studios, Emeryville
Matthias Teschner , University of Freiburg, Freiburg
We propose a novel formulation of the projection method for Smoothed Particle Hydrodynamics (SPH). We combine a symmetric SPH pressure force and an SPH discretization of the continuity equation to obtain a discretized form of the pressure Poisson equation (PPE). In contrast to previous projection schemes, our system does consider the actual computation of the pressure force. This incorporation improves the convergence rate of the solver. Furthermore, we propose to compute the density deviation based on velocities instead of positions as this formulation improves the robustness of the time-integration scheme. We show that our novel formulation outperforms previous projection schemes and state-of-the-art SPH methods. Large time steps and small density deviations of down to 0.01% can be handled in typical scenarios. The practical relevance of the approach is illustrated by scenarios with up to 40 million SPH particles.
Earth Observing System, Jacobian matrices, Equations, Convergence, Force, Mathematical model, Computational modeling, Three-Dimensional Graphics and Realism, Animation
M. Teschner, C. Horvath, B. Solenthaler, J. Cornelis and M. Ihmsen, "Implicit Incompressible SPH," in IEEE Transactions on Visualization & Computer Graphics.