Simulation - Smoothed-Particle Hydrodynamics

The objective is to model a fluid simulation using SPH model.
So far, only the gravity force is applied on the particles
The blue color around the particle comes from a field function set as \(f(p)=\sum_i exp\left(-\left(\|p-p_i\|/\sigma\right)^2\right)\) and displayed as a colored texture to give the visual impression of continuous fluid material. > Fill the function "update_density" that set the density at each particle position \(\rho_i\) using a smooth kernel

• • \(\displaystyle W_h(p) = \frac{315}{64\,\pi\,h^ 3}\,\left(1-\left(\frac{\|p\|}{h}\right)^ 2\right)^ 3\), \(\|p\|\leq h\)
  • Note that this kernel is already implemented in the function W_density.

> Complete the function "update_acceleration" to add the force component related to pressure and check that the solution seems reasonable (before adding viscosity forces).

• Note: Fill the function "W_gradient_pressure" to be the gradient of the spiky kernel and use it in the computation of the pressure force

> Add the viscosity component to the acceleration and observe the behavior for various viscosity (you may need to decrease the integration time step for large viscosity value).

Extensions

• - Note that particles have been initialized in the \((x,y)\) plane and leads to a 2D simulation. But if you initialize particles in 3D (or add a small \(z\) component in their initial position), the simulation will adapt seamlessly to 3D.

• - If you have spare time: Implement an acceleration grid structure to avoid comparing all pairs of particles (ex. uniform grid).