這真的好難懂，可以請高手用中文解釋一下這個式子在講什麼嗎?
感謝解惑!!
http://home.pchome.com.tw/world/blueharvest/WaterEquation01.jpg
http://home.pchome.com.tw/world/blueharvest/WaterEquation02.jpg
http://home.pchome.com.tw/world/blueharvest/WaterEquation03.jpg
1.以上第一個和第二、三都是水的公式，為什麼不太一樣?
2.這個公式和其中的符號和字母各代表什麼意思(中文解釋)?
第二和第三張圖附有下列文字說明:
主題，用電腦來模擬水的物理動態
Method Outline
The Navier-Stokes equations for describing the motion of a liquid
consist of two parts. The first, enforces incompressibility by
saying that mass should always be conserved, i.e. (如下兩圖)
http://home.pchome.com.tw/world/blueharvest/WaterEquation02.jpg
http://home.pchome.com.tw/world/blueharvest/WaterEquation03.jpg
This equation models the changes in the velocity field over time
due to the effects of viscosity 黏度(v), convection對流, density 密度(P),pressure壓力 (p), and gravity重力 (g). By solving (3.1) and (3.2) over time,
we can model the behavior of a volume of liquid. The new
algorithm we are proposing to do this consists of six
straightforward steps:
I. Model the static environment as a voxel grid. (Voxel Grid?不懂)
II. Model the liquid volume using a combination of
particles and an implicit surface (implicit surface? 不懂).
Then, for each simulation time step
III. Update the velocity field by solving 圖03 using finite
differences combined with a semi-Lagrangian method.
IV. Apply velocity constraints due to moving objects.
V. Enforce incompressibility by solving a linear system
built from 圖WaterEquation02 或 03
VI. Update the position of the liquid volume (particles and
implicit surface) using the new velocity field.
Velocity是不是當速率，但在圖
http://home.pchome.com.tw/world/blueharvest/WaterEquation03.jpg
這張圖裡，velocity好像又不是當速度解
因為在解釋步驟 I.的原文裡是講到 (下文)
Static Environment
Equations (圖2) and (圖3) model a liquid as two coupled dynamic
fields, velocity and pressure. The motion of the liquid we are
modeling will be determined by evolving these fields over time.
We start by representing the environment that we want the liquid
to move in as a rectangular grid of voxels with side length .o. The
grid does not have to be rectangular, but the overhead of unused
(non-liquid containing) cells will be low and so it is convenient.
Each cell has a pressure variable at its center and shares a velocity
variable with each of its adjacent neighbors (see figure 2). This
velocity is defined at the center of the face shared by the two
neighboring cells and represents the magnitude of the flow normal
to that face. This is the classic "staggered" MAC grid [15]. Each
cell is then either tagged as being empty (available to be filled
with liquid) or filled completely with an impermeable static
object. Despite the crude voxelized approximation of both objects
and the liquid volume itself, we'll show that we can still obtain
and track a smooth, temporally coherent liquid surface.
麻煩各位高手指點一下對物理很不拿手的小弟，感激不盡
詳全文，可以下列位址下載PDF:
http://graphics.stanford.edu/%7Efedkiw/papers/stanford2001-02.pdf
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