Digital Signal Processing Reference
In-Depth Information
Detail enhancement can also be achieved by irregular grid structure. In order to
capture details, Losassa et al. [11] proposed a grid method using octree data structure,
which lead to a good result. Dobashi et al. [12] proposed an overlapping grid method
to deal with the interaction between smoke and rigid obstacles. They generated local
fine grids based on global grid, and these fine grids moved along with obstacles.
However, the computational cost will increase with the increase amount of the ob-
stacles. Lentine et al. [13] accelerated the simulation by a mapping method between
coarse and fine grid. Pfaff et al. [14] proposed to add artificial boundary layer around
obstacles, and used a turbulence model to identify which regions of this layer will
transform into actual turbulence. It is efficient but hard to be applied to obstacles
which can deform like cloth. There are also other methods [15-16] to enhance fluid
details using improved mathematical method or solver. [17] gave a detailed summary
of the research status about fluid simulation.
3
Two-Scale Grid Method and Grid Division Scheme
In this section, we first give a brief overview about the incompressible N-S equations.
Then describe the method used in the two-scale grid simulation. Finally, we propose
the grid division scheme based on the vorticity field.
3.1
Incompressible Navier-Stokes Equations
Physically based fluid simulations are mostly based on the incompressible fluid N-S
equations shown as follows:
/
(1)
0
(2)
Equation (1) is momentum equation, where
denotes velocity,
t
denotes time,
is
pressure,
is density, and
f
represents external force, such as buoyancy and gravity.
Equation (2) is mass equation. It ensures the conservation of the fluid mass.
3.2
Two-Scale Grid Method
In theory, the richness of details is related to the grid resolution. The higher resolution
is the more details gets. As the increase of grid resolution, the computational cost
becomes higher. In this paper we first calculate the velocity on coarse grid to obtain
the general movement of the smoke. Then sample the velocity values to fine grid and
simulate to increase smoke details. Finally, sample the fine grid velocity back to the
coarse grid and obtain the final velocity. This method can avoid the large computa-
tional cost when simulate on global fine grid directly and lead to a good effect.
We use the method proposed in Stam [1] and Fedkiw et al. [2] to solve the N-S
equations in coarse grid, which divided the calculation into several steps: add external
