Streamline Diffusion
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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. Given an advection-diffusion equation, streamline diffusion refers to all diffusion going on along the advection direction. If we take an advection equation, for simplicity of writing we have assumed nablacdotmathbf{F}=0, and {bold u} =1 frac{partialpsi}{partial t} +{bold u}cdotnablapsi=0. we may add a diffusion term, again for simplicty, we assume the diffusion to be constant over the entire field. Dnabla^2psi, Giving us an equation on the form: frac{partialpsi}{part...
Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. Given an advection-diffusion equation, streamline diffusion refers to all diffusion going on along the advection direction. If we take an advection equation, for simplicity of writing we have assumed nablacdotmathbf{F}=0, and {bold u} =1 frac{partialpsi}{partial t} +{bold u}cdotnablapsi=0. we may add a diffusion term, again for simplicty, we assume the diffusion to be constant over the entire field. Dnabla^2psi, Giving us an equation on the form: frac{partialpsi}{partial t} +{bold u}cdotnablapsi +Dnabla^2psi =0 We may now rewrite the equation on the following form: frac{partialpsi}{partial t} +{bold u}cdot nablapsi +{bold u}({bold u}cdot Dnabla^2psi) +(Dnabla^2psi-{bold u}({bold u}cdot Dnabla^2psi)) =0 The term below is called streamline diffusion. {bold u}({bold u}cdot Dnabla^2psi)
