**[Position Based Fluids](https://dl.acm.org/doi/abs/10.1145/2461912.2461984)** Miles Macklin, Matthias Müller SIGGRAPH 2013  Abstract =================================================================== In fluid simulation, enforcing incompressibility is crucial for realism; it is also computationally expensive. Recent work has improved efficiency, but still requires time-steps that are impractical for real-time applications. In this work we present an iterative density solver integrated into the Position Based Dynamics framework (PBD). By formulating and solving a set of positional constraints that enforce constant density, our method allows similar incompressibility and convergence to modern smoothed particle hydro-dynamic (SPH) solvers, but inherits the stability of the geometric, position based dynamics method, allowing large time steps suitable for real-time applications. We incorporate an artificial pressure term that improves particle distribution, creates surface tension, and lowers the neighborhood requirements of traditional SPH. Finally, we address the issue of energy loss by applying vorticity confinement as a velocity post process. Preliminary Knowledge =================================================== This paper combines Position-based Dynamics and Smoothed Particle Hydrodynamics (SPH) methods for simulating incompressible fluids. In contrast to the traditional Lagrangian perspective of SPH, the interaction between fluid particles is transformed into PBD constraints, and fluid motion is simulated by solving fluid constraints.

So the preliminary papers shows below: - [Position Based Dynamics(PBD)](https://matthias-research.github.io/pages/publications/posBasedDyn.pdf) - [Predictive-Corrective Incompressible SPH(PCISPH)](https://people.inf.ethz.ch/~sobarbar/papers/Sol09/Sol09.pdf) Main Equation =================================================== Construct constraint type for fluid: \begin{equation}C_i(p_1, ..., p_n) = \frac{\rho_i}{\rho_0} - 1\end{equation}, which is same as other basic PBD constraint type on cloth. $C()$ Main Contribution =============================================================== Conclusion =================================================================== Future Ideas ===================================================================