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\input table_macro
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\centerline{\bf Estimate of  computational costs: 20 GFs Sustained Machine (optimal today)}
\bigskip
\line{Assume a 3D problem which: \hfill}
\smallskip
\item{$\bullet$} is computed for 50 turnover times,
\item{$\bullet$} uses 5 points to resolve the dissipation scales,
\item{$\bullet$} has 5 ($\rho,Vx,Vy,Vz,P$) + 2 (chemicals) = 7 variables,
\item{$\bullet$} uses 7 (physical) + 4 (scratch) = 11 arrays,
\item{$\bullet$} dumps 1000 snapshots,
\item{$\bullet$} performs 4,000 FP/grid point.
\medskip
\noindent
Use the estimate that the number of degrees of freedom required
to represent fully developed turbulence scales as $(L/l)^3 \sim Re^{9/4}$.

$$
\table
\tablespec{\c\c\c\c\c\c\c}
\body
{
\hline
| | | | | | | |\end
| N | Re | FP/Run | Nsteps | Core Mem. | Storage | Exec. Time |\end
| | | | |  (11 arrays) | (7 vars/1000 dumps)| |\end
\hline
| | | | | | | |\end
|$64^3$ | 30 | $6.2\ 10^{12}$ | 6,000 | 23 MB  | 15 GB | 5.2 mins |\end
| | | $1\ 10^9$FP/step | | |    | 0.05s/step |\end
\hline
| | | | | | | |\end
|$128^3$  | 75 | $1.1\ 10^{14}$ | 12,500 | 185 MB | 117 GB | 1.5 hrs |\end
| | | $8.3\ 10^9$FP/step | | |   |0.4s/step |\end
\hline
| | | | | | | |\end
|$256^3$ | 190 | $1.7\ 10^{15}$ | 25,000 | 1.5 GB | 939 GB | 23 hrs |\end
| | | $6.7\ 10^{10}$FP/step | | | | 3.4s/step  |\end
\hline
| | | | | | |  |\end
| $512^3$ | 480 | $2.7\ 10^{16}$ | 50,000 | 12 GB | 7.5 TB | 373 hrs |\end
| | | $5.4\ 10^{11}$FP/step | | | | 27s/step | \end
\hline
| | | | | | | |\end
|$1024^3$ | 1207 | $4.3\ 10^{17}$ | 100,000 | 94 GB | 60 TB | 6,000 hrs |\end
| | | $4.3\ 10^{12}$FP/step | | | | 214s/step  | \end
\hline
}
\endtable
$$
\bye
