- #1
Bucky
- 79
- 0
Hi, hope this is the right area. Also please excuse me completley ignoring the template, I don't think it's applicable for the problem.
I'm an honours year student in a comp sci course and I've decided to do an implimentation of Smooth Particle Hydrodynamics in a 3d application as my topic. Currently I'm trying to understand the Navier-Stokes equations and figure out how to break them down into variables and functions.
My two comparisons of the equation at the moment are a paper on the subject:
http://graphics.ethz.ch/Downloads/Publications/Papers/2003/mue03b/p_Mue03b.pdf
and the wikipedia article on navier stokes:
http://en.wikipedia.org/wiki/Navier-Stokes_equations
that muller 03 paper lists the navier-stokes equation as:
ρ (∂v / ∂t + v·∇v) = −∇p+ρg+μ∇2v,
(am I right in saying that ∂v / ∂t is just acceleration?)
whereas wikipedia gives it as:
ρ (∂v / ∂t + v·∇v) = −∇p + f +μ∇2v,
wheeere...
ρ = density
v = velocity
t = time
p = pressure
μ = viscosity
the notable change is f (representing external forces) to ρg. where, rho represents density, and g represents a density field(?).
firstly, I don't get these 'field' things. are they just the weighted average of certain variables of particles surrounding the particle we're currently looking at? is this what smoothing kernels are used for?
if i "solve" this equation, what do i actually end up with?
also the upside down triangle (grad?), represents the gradient of the element? how do you even find that?
I'm an honours year student in a comp sci course and I've decided to do an implimentation of Smooth Particle Hydrodynamics in a 3d application as my topic. Currently I'm trying to understand the Navier-Stokes equations and figure out how to break them down into variables and functions.
My two comparisons of the equation at the moment are a paper on the subject:
http://graphics.ethz.ch/Downloads/Publications/Papers/2003/mue03b/p_Mue03b.pdf
and the wikipedia article on navier stokes:
http://en.wikipedia.org/wiki/Navier-Stokes_equations
that muller 03 paper lists the navier-stokes equation as:
ρ (∂v / ∂t + v·∇v) = −∇p+ρg+μ∇2v,
(am I right in saying that ∂v / ∂t is just acceleration?)
whereas wikipedia gives it as:
ρ (∂v / ∂t + v·∇v) = −∇p + f +μ∇2v,
wheeere...
ρ = density
v = velocity
t = time
p = pressure
μ = viscosity
the notable change is f (representing external forces) to ρg. where, rho represents density, and g represents a density field(?).
firstly, I don't get these 'field' things. are they just the weighted average of certain variables of particles surrounding the particle we're currently looking at? is this what smoothing kernels are used for?
if i "solve" this equation, what do i actually end up with?
also the upside down triangle (grad?), represents the gradient of the element? how do you even find that?
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