# Smooth Particle Hydrodynamics

1. Oct 12, 2007

### Bucky

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 [Broken]

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?

Last edited by a moderator: May 3, 2017
2. Oct 12, 2007

### stewartcs

I believe that is the del operator...http://en.wikipedia.org/wiki/Del

3. Oct 13, 2007

### Bucky

ok i looked at that wiki article, and del is used to mean a lot of things. whats it supposed to be representing here? I noticed it has some relation to fields too :/

if i was planning to use this in an application, say to find the acceleration each frame. could i just rearrange the equation to get the acceleration term on it's own (or with velocity, since that'd be a known variable)?

4. Nov 28, 2011

### spider853

if you didn't found anything
I recommend you the fallowing papers:
http://liu.diva-portal.org/smash/get/diva2:324983/FULLTEXT01
Here they are showing some kernel functions

also a paper with a different (hack) approach that is easier to implement:
http://www.iro.umontreal.ca/labs/infographie/papers/Clavet-2005-PVFS/pvfs.pdf [Broken]

Last edited by a moderator: May 5, 2017
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