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\section{Flux-form momentum equations} |
\section{Flux-form momentum equations} |
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\label{sec:flux-form_momentum_eqautions} |
\label{sec:flux-form_momentum_eqautions} |
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\begin{rawhtml} |
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<!-- CMIREDIR:flux-form_momentum_eqautions: --> |
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\end{rawhtml} |
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The original finite volume model was based on the Eulerian flux form |
The original finite volume model was based on the Eulerian flux form |
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momentum equations. This is the default though the vector invariant |
momentum equations. This is the default though the vector invariant |
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The no-slip condition defines the normal gradient of a tangential flow |
The no-slip condition defines the normal gradient of a tangential flow |
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such that the flow is zero on the boundary. Rather than modify the |
such that the flow is zero on the boundary. Rather than modify the |
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stresses by using complicated functions of the masks and ``ghost'' |
stresses by using complicated functions of the masks and ``ghost'' |
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points (see \cite{Adcroft+Marshall98}) we add the boundary stresses as |
points (see \cite{adcroft:98}) we add the boundary stresses as |
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an additional source term in cells next to solid boundaries. This has |
an additional source term in cells next to solid boundaries. This has |
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the advantage of being able to cope with ``thin walls'' and also makes |
the advantage of being able to cope with ``thin walls'' and also makes |
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the interior stress calculation (code) independent of the boundary |
the interior stress calculation (code) independent of the boundary |
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\tau_{33} & = & A_v \frac{1}{\Delta r_f} \delta_k w |
\tau_{33} & = & A_v \frac{1}{\Delta r_f} \delta_k w |
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\end{eqnarray} |
\end{eqnarray} |
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It should be noted that in the non-hydrostatic form, the stress tensor |
It should be noted that in the non-hydrostatic form, the stress tensor |
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is even less consistent than for the hydrostatic (see Wazjowicz |
is even less consistent than for the hydrostatic (see |
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\cite{Waojz}). It is well known how to do this properly (see Griffies |
\cite{wajsowicz:93}). It is well known how to do this properly (see |
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\cite{Griffies}) and is on the list of to-do's. |
\cite{griffies:00}) and is on the list of to-do's. |
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\fbox{ \begin{minipage}{4.75in} |
\fbox{ \begin{minipage}{4.75in} |
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{\em S/R MOM\_U\_RVISCLFUX} ({\em mom\_u\_rviscflux.F}) |
{\em S/R MOM\_U\_RVISCLFUX} ({\em mom\_u\_rviscflux.F}) |
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