Class TimeIntegration

Class Documentation

class SPH::TimeIntegration

Class for the position-based fluids time integration.

Public Static Functions

void semiImplicitEuler(const Real h, const Real mass, Vector3r &position, Vector3r &velocity, const Vector3r &acceleration)

Perform an integration step for a particle using the semi-implicit Euler (symplectic Euler) method:

\[\begin{split}\begin{align*} \mathbf{v}(t+h) &= \mathbf{v}(t) + \mathbf{a}(t) h\\ \mathbf{x}(t+h) &= \mathbf{x}(t) + \mathbf{v}(t+h) h \end{align*}\end{split}\]

Parameters

  • h: time step size

  • mass: mass of the particle

  • position: position of the particle

  • velocity: velocity of the particle

  • acceleration: acceleration of the particle

void velocityUpdateFirstOrder(const Real h, const Real mass, const Vector3r &position, const Vector3r &oldPosition, Vector3r &velocity)

Perform a velocity update (first order) for the linear velocity:

\[\begin{equation*} \mathbf{v}(t+h) = \frac{1}{h} (\mathbf{p}(t+h) - \mathbf{p}(t) \end{equation*}\]

Parameters

  • h: time step size

  • mass: mass of the particle

  • position: new position \(\mathbf{p}(t+h)\) of the particle

  • oldPosition: position \(\mathbf{p}(t)\) of the particle before the time step

  • velocity: resulting velocity of the particle

void velocityUpdateSecondOrder(const Real h, const Real mass, const Vector3r &position, const Vector3r &oldPosition, const Vector3r &positionOfLastStep, Vector3r &velocity)