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	{\huge {\bf Boundary Condition Implementation}}
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\begin{itemize}

\item Implicit BCs are used in PUMA when any of the implicit 
time-integration schemes are used (i.e. the BC is evaluated at
the next timestep as opposed to the current timestep).

\item The boundary condition Jacobian $J_{BC}$ ($\frac{\partial Q_{BC}}
{\partial Q}$) is obtained numerically using central differences, which
is completely general and does much to improve the maintainability
of the code.

\item There are several types of BCs implemented in PUMA, and more
can be added without much difficulty as and when wanted.

\end{itemize}

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\begin{table}[h]
\begin{tabular}{|c|l|l|} \hline
{\bf Type}&{\bf Description}&{\bf Variable values specified} \\ \hline
0 & Do nothing & \\ \hline
1 & Fixed at freestream & \\ \hline
2 & Fixed at given values & $\rho$,$u$,$v$,$w$,$p$ \\ \hline
3 & First order extrapolation from the interior & \\ \hline
4 & Second order extrapolation from the interior & \\ \hline
5 & Inflow/outflow (Riemann) & \\ \hline
6 & Specified $p_0$, $T_0$ & $p_0$, $T_0$ \\ \hline
7 & Fixed back pressure pressure & $p$ \\ \hline
8 & Tangency & \\ \hline
9 & No slip adiabatic wall & \\ \hline
10 & No slip fixed�temperature wall $T_{wall}$ & $T_{wall}$ \\ \hline
11 & Zero $u$ velocity & \\ \hline
12 & Zero $v$ velocity & \\ \hline
13 & Zero $w$ velocity & \\ \hline

\end{tabular}
\end{table}
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