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1.3.8 Vector invariant form

For some purposes it is advantageous to write momentum advection in eq(1.1) and (1.2) in the (so-called) `vector invariant' form:

$\displaystyle \frac{D\vec{\mathbf{v}}}{Dt}=\frac{\partial \vec{\mathbf{v}}}{\pa...
...bf{v}}+\nabla \left[ \frac{1}{2}(\vec{\mathbf{v}}\cdot \vec{\mathbf{v}})\right]$ (1.44)

This permits alternative numerical treatments of the non-linear terms based on their representation as a vorticity flux. Because gradients of coordinate vectors no longer appear on the rhs of (1.44), explicit representation of the metric terms in (1.29), (1.30) and (1.31), can be avoided: information about the geometry is contained in the areas and lengths of the volumes used to discretize the model.

Copyright 2002 Massachusetts Institute of Technology