DOE calculator for simulation studies
How many simulations does your design study need? Compare seven DOE methods and their wall time on your hardware.
1Describe your study
Parameters you vary, 2 to 20.
Values tested per variable. Only the full factorial uses it.
Total cores ÷ cores per run.
Wall time of one simulation, from your solver log or an estimate.
Full factorial: every combination
runs
- Levelsk combinations
- –
- Wall time
- –
Every extra variable multiplies the count by the number of levels.
2Compare the methods
| Method | Runs | Wall time | Relative wall time |
|---|
Wall time = runs ÷ runs in parallel, rounded up to whole batches, × time per run. Add 5–15 % for start-up, queueing and failed runs.
Recommended starting point
–
- Runs
- –
- Wall time
- –
3See how the samples cover the space
Two of your variables, seen from above
Each dot is one simulation. On the grid each dot stands for Lk−2 runs that differ only in the other variables, and only L values per variable are ever tested. LHS places one sample in every row and column, random sampling leaves gaps and clusters, and R₂ spreads points evenly without a grid.
Search instead of map: Simcenter HEEDS
A static plan fixes every run before you start. Simcenter HEEDS picks each new design from the results so far and spends the budget where the good designs are.
Latin hypercube: a map of the space
- Runs
- –
- Wall time
- –
- You get
- How each variable acts
Simcenter HEEDS: a search for the best design
- Runs, illustrative
- –
- Wall time
- –
- You get
- A near-optimal design
The HEEDS figure is a planning estimate (35–55 % of the LHS count, at least 15), not a benchmark. About Simcenter HEEDS →
How to use the calculator
Enter how many design variables you want to vary, how many levels a full factorial would test for each, the wall time of one simulation and how many simulations you can run at the same time. The presets fill in four typical studies; you can change every field afterwards.
Step 1 shows the brute-force answer: the full factorial, every combination of every level. Step 2 compares it with the screening, response-surface and space-filling designs that answer most engineering questions with a few dozen runs, and suggests a starting point. Step 3 plots how the samples fill two of your variables and sets a static Latin hypercube against an adaptive search in Simcenter HEEDS.
Wall time counts whole batches: with four runs in parallel, 50 runs take 13 batches, not 12.5. Copy the comparison into a project plan or a hardware request. Links can also open the calculator with a preset filled in, for example the CFD preset.
Why a full factorial does not scale
A full factorial tests every combination of every level, so k variables at L levels need Lk runs. Two variables at three levels need 9 runs. Five variables at ten levels need 100,000, and ten variables at ten levels need ten billion.
At two hours per run and four runs in parallel, the 100,000-run study takes almost six years of wall time. Design of experiments exists to answer the same questions with a small, well-chosen subset of those runs.
The methods compared
The methods fall into three groups: two-level factorial designs for screening, response-surface designs for quadratic models, and space-filling designs for maps and surrogate models. Adaptive search is a fourth approach that looks for the best design instead of describing the whole space.
Fractional factorial: screening at two levels
A fractional factorial runs a chosen fraction of the two-level full factorial, 2k−p runs. The resolution tells you what is confounded. At resolution III, main effects are aliased with two-factor interactions. At resolution IV, main effects are clear but two-factor interactions are aliased with each other. At resolution V, all main effects and two-factor interactions can be estimated.
The calculator shows the smallest screening design (resolution III for three variables, IV from four) and, where it is larger, the smallest design of resolution V or higher for two-factor interactions. Six to eight variables can be screened in 16 runs, nine to sixteen in 32 and up to twenty in 64. With only two levels a fractional factorial cannot see curvature, so use it to find the variables that matter, not to model the response.
Central composite design (CCD): quadratic response surfaces
A CCD adds 2k axial points and a few centre runs to a two-level factorial core, which is enough to fit a full quadratic model with curvature and interactions. Up to four variables the core is the full 2k factorial. From five variables a resolution V fraction is enough, because a quadratic model needs main effects and two-factor interactions only: five variables take 16 + 10 + 6 = 32 runs instead of 48.
A CCD tests each variable at five levels: the factorial points at ±1, the centre and the axial points at ±α. With α > 1 the axial points lie outside the factorial range, so check that those designs can be meshed and solved, or use a face-centred design with α = 1. From nine variables the core is 128 runs, and a space-filling design or an adaptive search is usually cheaper.
Box–Behnken: three levels, no corners
Box–Behnken designs also fit quadratic models, but they use only three levels per variable and never set all variables to their extremes at the same time. That helps when the corners of the design space are hard to mesh, unphysical or likely to fail. The run counts here, 15, 27, 46 and 54 for three to six variables, include the usual 3, 3, 6 and 6 centre runs.
Latin hypercube sampling (LHS): fill the space
LHS splits the range of each variable into N equal intervals and places exactly one sample in every interval of every variable. The samples cover the full range of each variable without a grid and without assuming a shape for the response, which makes LHS the usual first plan for design-space maps and surrogate models.
A common rule of thumb is ten runs per variable (Loeppky, Sacks and Welch, 2009), and that is what the calculator uses. Check the surrogate against a few extra runs and add samples if the fit is poor. LHS treats every variable as a continuous range, so the number of levels does not apply.
Quasi-random sequences (R₂): even coverage you can extend
Low-discrepancy sequences such as Sobol, Halton or R₂ spread points more evenly than random sampling, and you can extend a sequence with more points later without redesigning the plan. The calculator gives them the same budget as LHS. The R₂ points in the plot use the plastic number, the two-dimensional counterpart of the golden ratio (Roberts, 2018).
Simcenter HEEDS: adaptive search
All the designs above are static: every run is fixed before the first one starts. Simcenter HEEDS uses SHERPA, a search that runs several global and local strategies at once and adapts them to the results so far, so the budget goes to the promising part of the design space.
That changes what you get. A Latin hypercube gives you a map of how each variable affects the response; an adaptive search gives you the best design it can find within the budget, not an even map. The HEEDS run count in the calculator is an illustrative planning figure of 35 to 55 % of the LHS count, and at least 15 runs. A real study needs as many runs as its objectives, constraints, noise and design space demand.
Choose a method
Start from the question you need answered, then check the run count against your compute budget. The run counts below are for six variables.
| Your question | Method | Runs, 6 variables |
|---|---|---|
| Which variables matter? | Fractional factorial, resolution IV | 16 |
| How do the important variables interact? | Fractional factorial, resolution V or higher | 32 |
| How curved is the response? | Central composite (2–10 variables) or Box–Behnken (3–6) | 50 or 54 |
| What does the whole design space look like? | Latin hypercube or R₂ sequence | 60 |
| What is the best design within the budget? | Adaptive search in Simcenter HEEDS | ~30, illustrative |
Many teams chain the methods: screen with a fractional factorial, drop the variables that do not matter, map the rest with LHS and let an adaptive search find the optimum in the most promising region.
Run-count formulas
The calculator uses these run counts for k design variables, L levels, a time trun per simulation and c runs in parallel.
N = Lk (1)
Full factorial: every combination of every level.
N = 2k−p (2)
Two-level fractional factorial. p is the largest value that still gives the resolution you need: NIST/SEMATECH section 5.3.3.4.7 up to 11 variables, and the published maximum-resolution tables (for example Montgomery, 2017) beyond that.
N = 2k−p + 2k + nc (3)
Central composite design: a full factorial core up to k = 4 and a resolution V core from k = 5, 2k axial points, and nc = 5, 6 or 8 centre runs for k ≤ 2, ≤ 6 and ≤ 10.
N = 15, 27, 46, 54 for k = 3, 4, 5, 6 (4)
Box–Behnken, including 3, 3, 6 and 6 centre runs.
N = 10k (5)
Starting budget for Latin hypercube and R₂ sampling (Loeppky, Sacks and Welch, 2009).
NHEEDS ≈ max(15, [0.55 − 0.2 min(1, (k − 2)/18)] NLHS) (6)
An illustrative planning figure, rounded to whole runs. It is not a property of the search algorithm.
twall = ⌈N / c⌉ trun (7)
Runs go in batches of c; ⌈ ⌉ rounds up to whole batches.
Assumptions: every run takes the same time, and a new batch starts when the previous one ends. Add 5–15 % for start-up, queueing and failed runs. The counts are for deterministic simulations; replicates and extra validation runs come on top. A full factorial is marked not feasible above one year of wall time.
Plan the compute
Runs in parallel
On a workstation with 32 to 64 cores, running each simulation on 8 to 16 cores gives two to eight runs at once, often two to four once memory bandwidth limits the scaling. A cluster makes 8, 16 or more possible. Because runs go in whole batches, a count just above a multiple of the parallel slots costs a full extra batch: 17 runs on 16 slots take as long as 32.
Time per run
Use the wall time of a converged run of a similar case, including meshing if the geometry changes with the design variables. For a transient case, count the full simulated time, not one time step.
Check the mesh before the sweep
Mesh the most extreme designs before you start the study. A grid study on one design with the GCI calculator tells you whether the differences between designs are larger than the discretization error, and the y+ calculator sizes a prism layer that suits every design.
Simcenter HEEDS with Simcenter STAR-CCM+
Simcenter HEEDS runs the whole loop for each design in Simcenter STAR-CCM+: it updates the geometry or the parameters, remeshes, solves, extracts the results and then decides on the next design. The same study can run a static plan such as a Latin hypercube or a fractional factorial, or an adaptive SHERPA search, and it can connect other CAE tools to the same workflow.
Volupe helps engineering teams go from the numbers in this calculator to a running study: a parameterised Simcenter STAR-CCM+ model, a design space that meshes reliably and a search strategy that fits the compute budget. Ask for a demo with your own problem.
References and changelog
References
NIST/SEMATECH e-Handbook of Statistical Methods, section 5.3.3.4.7, “Summary tables of useful fractional factorial designs”. itl.nist.gov
D. C. Montgomery, Design and Analysis of Experiments, 9th ed., Wiley, 2017: fractional factorial, central composite and Box–Behnken designs.
G. E. P. Box and K. B. Wilson, “On the experimental attainment of optimum conditions”, Journal of the Royal Statistical Society B 13(1), 1–45, 1951.
G. E. P. Box and D. W. Behnken, “Some new three level designs for the study of quantitative variables”, Technometrics 2(4), 455–475, 1960.
M. D. McKay, R. J. Beckman and W. J. Conover, “A comparison of three methods for selecting values of input variables in the analysis of output from a computer code”, Technometrics 21(2), 239–245, 1979.
J. L. Loeppky, J. Sacks and W. J. Welch, “Choosing the sample size of a computer experiment: a practical guide”, Technometrics 51(4), 366–376, 2009.
M. Roberts, “The unreasonable effectiveness of quasirandom sequences”, 2018. extremelearning.com.au
Review
Reviewed by Christoffer Johansson, M.Sc., Senior Application Specialist at Volupe. Version 2.0.
Changelog
October 2026: new interface in the CFD Handbook design. Run counts and wall times were checked automatically against the previous version, over two million comparisons. Corrections: the central composite design uses a resolution V core from five variables (32 instead of 48 runs for five variables, 88 instead of 280 for eight); fractional factorials show their resolution, with a separate screening design, and now cover up to 20 variables; wall time counts whole batches of parallel runs; a full factorial is recommended only when it needs no more runs than a Latin hypercube; the HEEDS figure is labelled as an illustrative estimate; and the quasi-random plot now shows the R₂ sequence, which the old plot drew as a single diagonal line.
Next in a CFD set-up
All CFD Handbook tools →GCI = Fs|ε| / (rp − 1)
Calculator
Grid Convergence Index (GCI) calculator
Check that the mesh resolves the differences between your designs before you run the study.
Open calculator →
k–ω SST · k–ε · S–A
Interactive guide
Turbulence model selector
Choose a turbulence model and wall treatment for your Simcenter STAR-CCM+ case, with the checks that go with it.
Open the selector →
y+ = uτy / ν
Calculator
y+ calculator
Size the first prism layer so every design in the study meets the same y+ target.
Open calculator →
Questions about DOE
Calculator reviewed by
Christoffer Johansson
Senior Application Specialist, M.Sc.
Planning a design study in Simcenter HEEDS or Simcenter STAR-CCM+? We reply within one day.
Ask a technical question →
What is design space exploration?
Design space exploration evaluates how changes to the design variables affect performance, using a structured set of simulations instead of changing one thing at a time. A DOE plan maps the space; an optimisation search looks for the best design in it. Each run goes through the same CAE workflow: pre-processing, solving and post-processing.
Why is a full factorial infeasible for many variables?
It tests every combination, Lk runs. Five variables at ten levels already need 100,000 simulations, and every extra variable multiplies the count by ten. Fractional factorials, response-surface designs and space-filling plans answer most questions with tens of runs.
How many samples does a Latin hypercube need?
A common starting point is ten runs per variable (Loeppky, Sacks and Welch, 2009), so 60 for six variables. Fit the surrogate model, check it against a few extra runs and add samples if the error is too large.
What does the resolution of a fractional factorial mean?
It tells you which effects are confounded. Resolution III aliases main effects with two-factor interactions. Resolution IV keeps main effects clear but aliases two-factor interactions with each other. Resolution V lets you estimate every main effect and two-factor interaction.
Why does the CCD need fewer runs here than with a full factorial core?
From five variables the factorial core of a central composite design can be a resolution V fraction, because a quadratic model only needs main effects and two-factor interactions. For five variables that gives 16 + 10 + 6 = 32 runs instead of 48, and for eight variables 88 instead of 280.
How many runs does Simcenter HEEDS need?
That depends on the problem: the number of variables, objectives and constraints, the noise and the shape of the design space. The calculator shows an illustrative planning figure of 35 to 55 % of the Latin hypercube count, and at least 15 runs. Set a budget and watch how the best design converges.
Does it work with Simcenter STAR-CCM+?
Yes. Simcenter HEEDS drives Simcenter STAR-CCM+ through geometry updates, meshing, solving and post-processing for every design. Volupe can help you set up the first study.
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