Water Simulation

Smoothed Particle Hydrodynamics

Navier-Stokes ekvationer

Applying Newton’s second law to fluid dynamics

• Conservation of mass
  
  $\frac{\partial {\rho}}{\partial{t}} + \nabla \cdot (\rho \textbf{v}) = 0$


• Conservation of momentum
  
  $\rho (\frac{\partial \textbf{v}}{\partial{t}} + \textbf{v} \cdot \nabla \textbf{v} ) = - \nabla p + \mu \nabla^2\textbf{v} + \rho \textbf{g}$
  
  Pressure-, viscosity- and external forces

Smoothed Particle Hydrodynamics (SPH)

• Calculation of a property $A$ at position $\textbf{r}$:
  
  $A_S(\textbf{r}) = \sum_{j}(m_j\frac{A_j}{\rho_j} W(\textbf{r} - \textbf{r}_j, h))$

Boundary conditions

Fluidparametrar

Smoothing kernels

Point-splatting