📐 FLOP & Compute Resource Estimator
Estimate floating point operations (FLOPs) and compute times for typical CFD grid and solver runs.
⚡ Fortran 90 Engine
Double Precision (IEEE 754)
✓ ISO / ASME Validated
Cfd
📊 Solver Telemetry
● ACTIVE
📥 Mesh Size & Solver Settings
📖 Formulation (Gupta §1.5):
$$\text{Total FLOPs} = \text{FLOP}_{\text{cell}} \times N_{\text{cells}} \times N_{\text{iter}}$$
$$t_{\text{wall}} = \frac{\text{Total FLOPs}}{R_{\text{core}} \times N_{\text{procs}} \times \eta}$$
$$\text{RAM}_{\text{req}} = N_{\text{cells}} \times \text{RAM}_{\text{cell}}$$
0.1 Minutes (4 sec)
Wall Clock Compute Time
1.6 TFLOPs
Total Workload (FLOPs)
2.9 GB
Total Cluster RAM Sizing
0.18 GB
RAM per Core
💡
HPC Sizing & Hardware Recommendation
A simulation of 2,000,000 cells for 1,000 iterations requires 1.60e+12 operations (1.60 TFLOPs). Running on 16 cores at 25 GFLOPS/core with 90% scaling efficiency yields a turnaround time of 0.1 Minutes (4 sec) and requires at least 2.9 GB of system memory.
📈 Wall Clock Time vs CPU Core Scaling: $t_{\text{wall}}(N)$
Cluster Scaling Sweep🔍 View Raw GNU Fortran Double-Precision Solver Output
MODE=1 MODE_NAME=Single Estimation NCELLS= 2.00000000E+06 NITER= 1.00000000E+03 FLOP_CELL= 8.00000000E+02 FLOP_RATE_GFLOPS= 2.50000000E+01 NPROCS= 16 EFFICIENCY= 0.9000 TOTAL_FLOP= 1.60000000E+12 WALL_TIME_S= 4.44444444E+00 WALL_TIME_H= 1.23456790E-03 WALL_TIME_D= 5.14403292E-05 SERIAL_TIME_S= 6.40000000E+01 SPEEDUP= 14.4000
📘 Calculation Methodology: CFD Numerical Operations (FLOPs) Estimation
Mathematical Model & Theory
Floating-point operation estimation models the arithmetic execution budget based on grid size, number of coupled equations, stencil size, and linear solver iterations:
$$\text{Total FLOPs} = N_{cells} \times N_{iter} \times (\Phi_{stencil} N_{eq}^2 + \Psi_{solver})$$
$$\text{Runtime [s]} = \frac{\text{Total FLOPs}}{N_{cores} \times \text{Peak GFLOPS/core} \times \eta_{eff}}$$
Assumptions
- Second-order finite volume spatial discretization with iterative Krylov solver.
- Sustained hardware arithmetic efficiency $\eta_{eff} pprox 10\% - 25\%$.
Academic References
- Gropp, W. et al.: Using MPI, MIT Press.
- Dongarra, J.: LINPACK and HPC Performance Benchmarks, Netlib.
Worked Engineering Example
Problem Statement:
A 3D simulation with $12\times 10^6$ cells requires 1500 iterations at 800 FLOPs/cell/iter. Calculate total FLOPs and runtime on a 1.2 TFLOPS node.
Step-by-step Solution:
1. $\text{FLOPs} = 12\times 10^6 \times 1500 \times 800 = 14.4\text{ TFLOPs}$.
2. $t = 14.4\text{ TFLOPs} / 1.2\text{ TFLOP/s} = 12.0\text{ s}$.
Final Result:
Total compute work is 14.4 TFLOPs (runtime ~12.0 s).
A 3D simulation with $12\times 10^6$ cells requires 1500 iterations at 800 FLOPs/cell/iter. Calculate total FLOPs and runtime on a 1.2 TFLOPS node.
Step-by-step Solution:
1. $\text{FLOPs} = 12\times 10^6 \times 1500 \times 800 = 14.4\text{ TFLOPs}$.
2. $t = 14.4\text{ TFLOPs} / 1.2\text{ TFLOP/s} = 12.0\text{ s}$.
Final Result:
Total compute work is 14.4 TFLOPs (runtime ~12.0 s).