Maya Shaders

Tuesday, September 06, 2005

Navier - Stokes Eqn on Fluid Behaviour

Navier Stokes (NS) Equations tries to define a method of fluid (liquid) behaviour.

Limitations of NS

  • continuous vol of fluid on a 2D rectangular domain
  • no interaction between air / sloshing water

Maths Background

Behaviour of fluids : Velocity Eqns -> determines how the fluid moves itself & the things that are on it.

Nature of fluids : Velocity varies on both time and space -> represent using a 'vector field'

Vector Field

Assumptions : -> on a 2D cartesian of M by N (M columns by N rows)

  • For every position vector x = (x,y) on vector field
  • Associated Velocity at time t -> u(x,t) = [u(x,t), v(x,t), w(x,t)]

Key is to think in time steps -> if we are able to calculate the u at the current velocity field, then we can move objects and smoke densities.

We assume an incompressible(volume constant in time), homogeneous(density rho constant in space) fluid.

Variables

x(x,y) : vector for 2d coordinate (cartesian grid)
u(x,t) : velocity field
p(x,t) : pressure/scalar field

At time t = 0, if u and p are known,

Fluid behaviour = Advection (velocity of e field carrying itself & others along the flow) + Pressure (molecules interaction with each other) + Diffusion (viscosity - how resistive a fluid is to flow -> resistance = diffusion of momentum) + External Forces (e.g. gravity)

References taken from GPU GEMS

1 Comments:

  • At 11:30 AM, Anonymous Anonymous said…

    wah u still blog !

     

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