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Streamline diffusion : ウィキペディア英語版
Streamline diffusion

Streamline diffusion, given an advection-diffusion equation, refers to all diffusion going on along the advection direction.
==Explanation==
If we take an advection equation, for simplicity of writing we have assumed \nabla\cdot=0, and ||||=1
:
\frac
+\cdot\nabla\psi=0.

we may add a diffusion term, again for simplicty, we assume the diffusion to be constant over the entire field.
:D\nabla^2\psi,
Giving us an equation of the form:
:
\frac
+\cdot\nabla\psi
+D\nabla^2\psi
=0

We may now rewrite the equation on the following form:
:
\frac
+\cdot \nabla\psi
+(\cdot D\nabla^2\psi)
+(D\nabla^2\psi-(\cdot D\nabla^2\psi))
=0

The term below is called streamline diffusion.
:(\cdot D\nabla^2\psi)

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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