| 4 |
\section{Vector invariant momentum equations} |
\section{Vector invariant momentum equations} |
| 5 |
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|
| 6 |
The finite volume method lends itself to describing the continuity and |
The finite volume method lends itself to describing the continuity and |
| 7 |
tracer equations in curvilinear coordinate systems but the appearance |
tracer equations in curvilinear coordinate systems. However, in |
| 8 |
of new metric terms in the flux-form momentum equations makes |
curvilinear coordinates many new metric terms appear in the momentum |
| 9 |
generalizing them far from elegant. The vector invariant form of the |
equations (written in Lagrangian or flux-form) making generalization |
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momentum equations are exactly that; invariant under coordinate |
far from elegant. Fortunately, an alternative form of the equations, |
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transformations. |
the vector invariant equations are exactly that; invariant under |
| 12 |
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coordinate transformations so that they can be applied uniformly in |
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|
any orthogonal curvilinear coordinate system such as spherical |
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coordinates, boundary following or the conformal spherical cube |
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system. |
| 16 |
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|
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The non-hydrostatic vector invariant equations read: |
The non-hydrostatic vector invariant equations read: |
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\begin{equation} |
\begin{equation} |
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