LES and DES Affordability Calculator: Cells, Time Steps and Core-Hours

Whether a scale-resolving run is affordable, answered before a week of cluster time is committed. Cell count, time step, step count and core-hours for wall-resolved LES, wall-modelled LES and DES, with the Reynolds-number exponent derived rather than quoted, and an honest statement of what the estimate does not know.

Last updated 30 Sep 2026

LES and DES affordability

Reynolds number, domain and approach → cells, time steps, core-hours and a verdict

Free-stream velocity U (m/s)The velocity the Reynolds number and the flow-through time are built on. For an internal flow use the bulk velocity and put the hydraulic diameter in the length box.

Streamwise length L (m)The length the boundary layer develops over: the chord, the body length, the duct length. It sets both the Reynolds number and the flow-through time L/U, so it is the single most influential input on this page.

Kinematic viscosity ν (m²/s)1.516×10⁻⁵ m²/s for air at 20 °C and 101.325 kPa; 1.004×10⁻⁶ for water at 20 °C. At altitude or in a heated flow this moves a long way and the cell count moves with it to the power of nearly two.

Wetted area to be resolved A_w (m²)The surface area whose boundary layer has to be meshed — both sides of a 1 m square plate is 2 m². For a wing, twice the planform area is a good first estimate; for a car, roughly four times the frontal area. Cell count is directly proportional to this, so it is worth getting right to within 30%.

ApproachThis is the choice that decides whether the run is possible. The three differ not by a constant factor but by their exponent on Reynolds number, so the gap between them widens without limit as the Reynolds number rises. The figures underneath show what each of the three would cost for the same case.

Transition Reynolds number Re_x0Where the boundary layer becomes turbulent, as a Reynolds number based on distance from the leading edge. Around 5×10⁵ on a smooth flat plate at low free-stream turbulence; 10⁵ or less with roughness, a trip or high inlet turbulence; 10⁶ and beyond on a favourable pressure gradient. It matters more than it looks: the cell count is set by an integral that is dominated by the most upstream turbulent station, because that is where the cells are smallest.

Streamwise spacing in wall units Δx⁺Wall-resolved LES only. 50 to 100 is standard practice; wall-resolved LES aiming at the near-wall streak structure uses 20 to 50. This and Δz⁺ enter the cell count as 1/(Δx⁺·Δz⁺), so relaxing both by a factor of two cuts the mesh by four.

Spanwise spacing in wall units Δz⁺Wall-resolved LES only. 15 to 30 is the usual range. The spanwise direction has to be finer than the streamwise one because the near-wall streaks are about 100 wall units apart in z and roughly a thousand long in x.

Cells across the boundary layerWall-normal cells from the wall to the edge of the boundary layer. 25 to 40 is normal for wall-resolved LES with the first cell at y⁺ ≈ 1, and 20 to 30 for wall-modelled LES. The wall-normal direction is cheap compared with the other two, so this is rarely where to economise.

Cells per boundary-layer thickness in x and zWall-modelled LES and DES only: the streamwise and spanwise spacing expressed as δ/Δ. Common practice is 10 to 20. It enters the cell count squared, so this is the most expensive single number on the page for a wall-modelled run — and the Pope resolution measure below tells you whether the value you chose actually resolves the energy you think it does.

Fraction of the wetted area in the LES focus regionDES only. The part of the surface where the flow separates and the LES branch is actually doing work, and therefore where the full spanwise resolution is needed. The rest is attached boundary layer running in RANS mode, where this page assumes the streamwise and spanwise spacing can be four times coarser — a stated modelling choice, not a measured one.

Off-body and wake multiplierEverything this page’s boundary-layer integral does not count: the wake, the separated region away from the surface, volumetric refinement, the far field. 1.3 to 2 for an attached external case; 2 to 4 when a long resolved wake is the point of the simulation. There is no way to derive this — it comes from a mesh, and the page asks for it rather than hiding a guess inside the answer.

Flow-through times to simulatePhysical time expressed in units of L/U. Allow a few to flush the initial transient and then enough to average over: 10 is thin, 20 to 40 is normal for forces, and second-order statistics or a spectrum want considerably more. This scales the bill linearly and it is usually the cheapest thing to argue about.

Target Courant numberScale-resolving runs target a maximum Courant number of about 1 whatever the time scheme, because there is no point resolving an eddy in space and then advecting it several cells in one step. The time step here is taken on the SMALLEST streamwise cell at the free-stream velocity, which is the conservative reading of the constraint.

Cores availableUsed for the wall-clock estimate and for the cells-per-core figure. Parallel efficiency is not modelled here; the companion memory and runtime page does that with Amdahl’s law and a cells-per-core band.

Core-hour budgetWhat you have to spend. The headline is the estimated cost divided by this, so 1.0 means exactly on budget. Given that the cell-count estimate is good to about a factor of two, treat anything between 0.5 and 2 as “too close to call”.

Core time per cell per time step (µs)Microseconds of single-core time to advance one cell by one time step, inner iterations included. About 1 to 3 µs for a well-optimised incompressible finite-volume LES, 5 to 20 µs for an implicit solver doing several inner iterations per step, and far more with combustion or Lagrangian particles. This is the one input that cannot be derived — measure it from a short run on the real mesh and the real machine.

Integral length scale as a fraction of δUsed only for the Kolmogorov, Taylor and Pope figures. In the outer part of a turbulent boundary layer the integral scale is a few tenths of δ; 0.3 is a reasonable default and 0.2 to 0.5 covers the usual claims. Pope’s resolution measure is proportional to this to the power minus two thirds, so the choice matters and it is exposed rather than buried.

0.514× budgetExample

Air at 20 °C over a 1 m body at 50 m/s, 2 m² of wetted area, wall-modelled LES with 15 cells per boundary-layer thickness and 30 across it, transition at Re_x = 5×10⁵, 20 flow-through times, 512 cores, a 20,000 core-hour budget and 2 µs per cell per step

Where the cell count comes from, and where the exponents come from

c_f = 0.027 Re_x^−1/7 · δ/x = 0.16 Re_x^−1/7 · u_τ = U√(c_f/2) · wall-resolved: N = (A_w/L) (N_y/Δx⁺Δz⁺) ∫(u_τ/ν)² dx → N ∝ Re_L^13/7 · wall-modelled: N = (A_w/L) n_xz²N_y ∫dx/δ² → N ∝ Re_L · Δt = CFL Δx_min/U · core-hours = N N_t c · M = C_K(Δ/π&ell;)^2/3

c_f: local skin friction coefficient. White’s turbulent flat-plate correlation, 0.027 Re_x^(−1/7), is the one used here; it tracks Schlichting’s logarithmic fit to within 5% from Re_x = 10⁶ to 10⁹, where the older one-fifth power law is 11% to 35% low
u_τ: friction velocity. Every near-wall length in a wall-resolved LES is ν/u_τ, so the cell count carries u_τ squared in two directions and the whole Reynolds-number scaling comes out of the c_f correlation
δ: boundary-layer thickness. For a wall-modelled run the spacing is proportional to δ rather than to ν/u_τ, and that single substitution is what turns the exponent from 13/7 into 1
Δx⁺, Δz⁺: streamwise and spanwise spacing in wall units, for the wall-resolved case. Standard practice is 50 to 100 and 15 to 30; the cell count is inversely proportional to their product
n_xz: cells per boundary-layer thickness in x and z, for the wall-modelled and DES cases. It enters the count squared
N_t: number of time steps, from the physical time divided by the step the Courant condition allows on the smallest streamwise cell
M: Pope’s measure of LES resolution: the fraction of turbulent kinetic energy left in the residual motions. Pope’s criterion is M below about 0.2. Evaluated here for a Kolmogorov inertial-range spectrum with C_K = 1.5, a cutoff wavenumber π/Δ and ε = u′³/ℓ
η, λ: Kolmogorov length (ν³/ε)^(1/4) and Taylor microscale √(15νu′²/ε). η/ℓ = Re_t^(−3/4) and λ/η = √15·Re_t^(1/4), both of which the calculator’s figures satisfy identically

Worked example

Air at 20 °C over a 1 m body at 50 m/s, 2 m² of wetted area, wall-modelled LES with 15 cells per boundary-layer thickness and 30 across it, transition at Re_x = 5×10⁵, 20 flow-through times, 512 cores, a 20,000 core-hour budget and 2 µs per cell per step
Re_L = U·L/ν = 50 × 1/1.516×10⁻⁵ = 3.30×10⁶. At x = L the skin friction from White's correlation is c_f = 0.027·Re_L^(−1/7) = 0.003164, so u_τ = U√(c_f/2) = 1.989 m/s and the boundary layer is δ = 0.16·L·Re_L^(−1/7) = 18.7 mm thick, which is 2,459 viscous lengths. That number, δ⁺, is the scale separation the simulation has to span, and it is what makes the difference between the three approaches
WALL-MODELLED LES first, because it is what was chosen. The spacing is proportional to δ, so the surface cell count is the integral of dx/δ² across the turbulent part of the plate, times the cells per δ squared, times the cells across δ. The integral has a closed form and it converges at the downstream end — which is why nearly all of the answer is set by conditions just after transition, where δ is thinnest. Result: 153 million boundary-layer cells, times the 1.5 off-body multiplier, 230 million cells
WALL-RESOLVED LES for comparison. Now the spacing is fixed in wall units, so the surface density goes as (u_τ/ν)² instead, and the same integral gives 1.21 billion cells — 5.3 times the wall-modelled figure at this Reynolds number. The ratio is not a constant: it grows as Re_L to the power 13/7 − 1 = 6/7, so at Re_L = 10⁸ it is about 92 and at 10¹⁰ about 4,700
AND DNS, to put the other two in scale. Wall-unit spacing through the whole boundary layer at Δx⁺ = 10, Δz⁺ = 5, Δy⁺ = 1 is the same integral with one further power of u_τ/ν, which is where the 37/14 exponent comes from: 1.5×10¹² cells. Six thousand times the wall-modelled mesh, for a 1 m body at a Reynolds number of three million
THE TIME STEP, taken conservatively. The smallest streamwise cell is not at x = L but just after transition, where δ is 3.72 mm and the cell is δ/15 = 0.248 mm. At a Courant number of 1 and the free-stream velocity that is Δt = 4.96×10⁻⁶ s. Twenty flow-through times is 20 × L/U = 0.4 s of physical time, so 80,620 time steps
THE BILL. 230 million cells × 80,620 steps × 2 µs = 3.70×10⁷ core-seconds = 10,289 core-hours, which on 512 cores is 20.1 hours of wall clock if the code scales perfectly. Against a 20,000 core-hour budget that is 0.514, so it fits — but only by a factor of two, which is the accuracy of the estimate, so this is a case for measuring the cost per cell per step on a short run before committing
HOW FAST IT RUNS AWAY. The local exponent d ln N / d ln Re_L for the wall-modelled model is 1.251 here, heading for its asymptote of exactly 1 as the laminar run-in becomes a small fraction of the plate. Add one power for the number of time steps and the core-hours go as Re_L to the power 2.25 at this point: 178 times the cost per decade of Reynolds number. The same case wall-resolved would climb on 13/7 + 1 = 2.86, which is about 720 times per decade
AND DOES IT DESERVE THE NAME. δ/15 at x = L is a filter width of 1.25 mm, 31.5 Kolmogorov lengths and 1.56 Taylor microscales. Pope's resolution measure comes out at M = 0.257: the subgrid model is being asked to supply 26% of the turbulent kinetic energy, against Pope's criterion of 20%. Getting under it would need 21.8 cells per δ rather than 15, which is 2.1 times the cells and would put the run over budget. That is a real trade-off and the page states it rather than resolving it — and note that the 21.8 depends on the integral length scale having been taken as 0.3δ; at ℓ = δ the requirement would be 6.5 cells per δ instead, which is why that assumption is an input

How the grid-point requirement scales with Reynolds number, and who worked it out

The difference between Chapman’s 9/5 and Choi and Moin’s 13/7 is one substitution: c_f as Re_x to the power minus one fifth against Re_x to the power minus one seventh. The second is the better correlation above Re_x of about 10⁶, and the whole revision follows from it. The two wall-modelled entries are the same result read two ways and both appear in the literature: with the transition station held at a fixed Reynolds number the count is linear in Re_L, and with transition at a fixed fraction of the body length the same integral gives 2/7, which is the figure in Choi and Moin’s own abstract. This page uses the first, because a transition Reynolds number is what a user can actually supply. The core-hour column adds one power of Re_L for the number of time steps, derived on this page’s own time-step model.
Approach	Exponent on Re_L	Source	Cells per decade of Re	Core-hours per decade
DNS	37/14 ≈ 2.643	Choi & Moin 2012; reproduced by derivation here	440×	4,400×
Wall-resolved LES	13/7 ≈ 1.857	Choi & Moin 2012	72×	720×
Wall-resolved LES, Chapman’s 1979 figure	9/5 = 1.800	Chapman 1979, superseded	63×	630×
Wall-modelled LES, transition at a fixed Re_x	1	Choi & Moin 2012 read with x₀ fixed	10×	100×
Wall-modelled LES, transition at a fixed fraction of L	2/7 ≈ 0.286	Choi & Moin 2012, as their abstract states it	1.9×	19×
DES or DDES	1, same as wall-modelled	follows from δ-proportional spacing	10×	100×

Resolution settings that go with each approach

Wall-resolved LES and DES both put the first cell at y⁺ of about 1 and differ in what happens in the streamwise and spanwise directions — which is exactly where the cells are, so it is where the cost is. A DES mesh with LES-quality spanwise resolution everywhere is a wall-resolved LES mesh with a RANS model on it, and costs accordingly; the saving comes from letting the attached region keep RANS-style anisotropic cells. The first-cell height in each case is the subject of the y⁺ and prism-layer pages.
Approach	First cell	Δx, Δz	Cells across δ	What the model is doing
Wall-resolved LES	y⁺ ≈ 1	Δx⁺ 50–100, Δz⁺ 15–30	25–40	subgrid model only; the near-wall streaks are resolved
Wall-modelled LES	first cell in the log layer	δ/10 to δ/20	20–30	a wall model supplies the shear stress from a matched log-layer velocity
DES / DDES / IDDES	y⁺ ≈ 1	δ/10 to δ/20 in the focus region	25–40	RANS across the attached boundary layer, LES where the flow separates
DNS	Δy⁺ ≈ 0.3 to 1	Δx⁺ ≈ 10, Δz⁺ ≈ 5	everything	nothing; every scale is resolved

The exponent is the answer: why wall modelling is not a saving but a change of scaling

The question this page answers is not “what mesh do I need” but “can I afford this at all”, and the honest answer usually turns on one number: the exponent on Reynolds number. Everything else — resolution settings, flow-through times, the cost per cell per step — moves the answer by a factor of a few. The exponent decides whether a case is a week on a departmental cluster or a year on a national facility, and it is different for each approach by a margin that widens without limit as the Reynolds number rises.

The exponents, and where they come from. Chapman set out the wall-resolved estimate in 1979 and got N proportional to Re_L to the power 9/5. Choi and Moin revisited it in Physics of Fluids in 2012 with better boundary-layer correlations and got 13/7 for wall-resolved LES, and a linear scaling for wall-modelled LES. The change is one substitution: Chapman used a skin-friction law going as Re_x to the power minus one fifth, Choi and Moin used one going as Re_x to the power minus one seventh, and the second is much the better correlation at high Reynolds number — it stays within about 5% of Schlichting’s logarithmic fit from Re_x of 10⁶ to 10⁹, where the one-fifth law runs 11% to 35% low. The derivation is short enough to state. Near-wall spacing in a wall-resolved LES is fixed in wall units, so the cell count per unit area goes as (u_τ/ν)², and u_τ² goes as c_f U². Integrate that along the plate, put the wetted area in, and the powers of Reynolds number come out as 1 + 6/7 = 13/7. For a wall-modelled run the spacing is proportional to δ instead, the integral becomes one of dx/δ², and the same algebra gives 1. This page recomputes both integrals from the correlations rather than applying a quoted exponent, then differentiates the result analytically and prints the local exponent — which is why the exponent on screen is above 13/7 at modest Reynolds number and settles onto it as the laminar run-in becomes a small fraction of the plate.

One thing about the wall-modelled exponent worth knowing before you quote it. Choi and Moin’s own abstract states the wall-modelled requirement as Re_L to the power 2/7, and later work quotes it as linear in Re_L. Both are right and it is the same integral: ∫dx/δ² converges at the downstream end and is dominated by the most upstream turbulent station, so the answer depends on where that station is. Hold the transition Reynolds number fixed and the count is linear in Re_L; let transition sit at a fixed fraction of the body length and the same expression gives exactly 2/7. This page asks for a transition Reynolds number and therefore reports the linear branch, and the 2/7 result drops straight out of the same formula if you scale Re_x0 with Re_L yourself. For a real vehicle, transition sits where a trip, a joint or a pressure gradient puts it, which is closer to a fixed Reynolds number than to a fixed fraction — but it is worth knowing why two reputable sources appear to disagree by a factor of three and a half in the exponent.

What the estimate does not account for, stated plainly, because a cell count to four significant figures would be a lie. It counts boundary-layer cells over a wetted area and multiplies by a factor you supply for the wake and the off-body region. It does not know about your geometry: curvature, corners, junctions, gaps, a landing-gear bay or a wing-body fillet all need cells that no boundary-layer integral will predict. It assumes a zero-pressure-gradient flat-plate boundary layer, so it will understate a case with strong adverse gradients — where δ grows faster and c_f falls faster than the correlation — and overstate a strongly accelerating one. It assumes transition happens at one station and is instantaneous. It ignores mesh-quality padding, buffer layers between refinement levels, and the cells a mesher inserts because it cannot do what you asked. Treat the number as good to a factor of two and ask whether the decision changes across that factor; if it does, the answer is that you need a measurement, not a better estimate.

The time step, and why it is the conservative one. Scale-resolving simulation wants a Courant number of about 1 — resolving an eddy on the grid and then advecting it several cells in a step throws away what the grid bought. The step here is taken on the smallest streamwise cell in the mesh, at the free-stream velocity. That is deliberately the worst case: the smallest streamwise cell is at the most upstream turbulent station, where u_τ is highest and δ is thinnest, and a solver reporting a maximum Courant number will find it there. Taking the step from the cell at x = L instead, as some published cost estimates do, gives a step several times larger and a cost estimate several times smaller, and the difference is not a disagreement about physics but about which cell you looked at. The band structure and the reasons behind a target of 1 are set out on the Courant number and time step page.

Kolmogorov, Taylor and Pope: three checks on whether what you are running deserves the name. The Kolmogorov length η = (ν³/ε)^(1/4) is the scale at which viscosity takes over, and the ratio Δ/η tells you how far above it the grid sits — a few hundred for a wall-modelled LES, tens for a wall-resolved one, and about one for DNS. The Taylor microscale λ = √(15νu′²/ε) sits between the two and is mostly useful as a sanity check: the calculator’s η, λ and turbulence Reynolds number satisfy η/ℓ = Re_t^(−3/4) and λ/η = √15·Re_t^(1/4) identically, which is a quick way to see that the scales are consistent. The one that is an actual criterion is Pope’s: M, the fraction of the turbulent kinetic energy left in the residual motions, should be under about 0.2 for a simulation to be called a large-eddy simulation rather than a very fine unsteady RANS. Computed for an inertial-range spectrum with C_K = 1.5, a cutoff at π/Δ and ε = u′³/ℓ, this comes out as M = C_K(Δ/πℓ)^(2/3), and it is worth being blunt about the sensitivity: M goes as the integral length scale to the power minus two thirds, so assuming ℓ = δ instead of ℓ = 0.3δ moves the required cells per δ from about 7 to about 21. The second figure is the one that matches what wall-modelled LES practice actually uses, which is a point in favour of the smaller integral scale — but the coefficient is convention-dependent by a factor of about two and this page exposes the assumption as an input rather than burying it.

What to do when the answer is no. In order of how much they give: change the approach, because that changes the exponent; cut the flow-through count, because that is linear and is often set by habit; relax the streamwise and spanwise spacing, because for a wall-modelled run that enters squared; and only then look at the wall-normal count, which is linear and is the cheapest direction you have. What almost never helps is buying more cores — the cost in core-hours is unchanged and, past a few thousand cells per core, the parallel efficiency starts working against you. The memory and runtime page puts Amdahl’s law and a cells-per-core band on that side of it.

Frequently asked questions

Is the Reynolds number exponent really 1.8 to 2.7 for LES?

No, and the range is worth unpicking because those two numbers each belong somewhere else. 1.8 is Chapman’s 1979 wall-resolved estimate, 9/5, which Choi and Moin superseded in 2012 with 13/7 = 1.857. 2.7 is close to the DNS exponent, 37/14 = 2.643, which is not an LES figure at all. And the range leaves out the number that matters most: wall-modelled LES scales linearly in Re_L, an exponent of 1, which is why it is the only route to high Reynolds number and why the gap between the two LES approaches widens without limit. The honest range for LES is 1 to 13/7, with 37/14 above it for DNS.

How accurate is the cell count?

Treat it as a factor of two. It is a boundary-layer integral over a wetted area, with a multiplier you supply for everything else, and it knows nothing about your geometry. What it is good at is ratios: the wall-resolved to wall-modelled ratio, the change when the Reynolds number moves, the change when you relax the spanwise spacing. Those are all differences of the same estimate and the systematic errors largely cancel, which is why the page prints all three approaches side by side rather than one number on its own.

Why does the transition Reynolds number change the answer so much?

Because the integrals are dominated by the most upstream turbulent station. Cells are smallest where u_τ is largest and δ is thinnest, which is immediately after transition, so moving transition upstream adds the most expensive part of the plate. For wall-modelled LES the effect is stronger still: the integral ∫dx/δ² converges downstream, so essentially the whole cell count is set by conditions near x₀. Tripping a boundary layer at Re_x of 10⁵ instead of 5×10⁵ is not a small change to the mesh.

Should the time step come from the smallest cell or from a typical one?

From the smallest, if you are running one global time step, because that is where the solver’s reported maximum Courant number will come from. This page uses the smallest streamwise cell at the free-stream velocity, which is conservative in two ways: the velocity in the smallest near-wall cell is well below the free stream, and a local Courant number there will be lower than the figure used here. If your solver does local time stepping, or if you are willing to accept a Courant number above 1 in a small part of the domain, the step can be larger and the cost falls proportionally. Cutting the step is the one economy that is exactly linear in both directions.

Can I get the cost down by using more cores?

Not in core-hours, which is what a budget is usually denominated in — more cores buys wall clock, not cost, and past a point it costs you both. Below roughly 10,000 cells per core the parallel efficiency begins to fall away and below about 2,500 it falls quickly; at that point adding cores increases the core-hours consumed while barely reducing the wall clock. The wall-clock figure on this page assumes perfect scaling, so it is optimistic by exactly the parallel inefficiency.

What is a realistic cost per cell per time step?

1 to 3 microseconds of single-core time for a well-optimised incompressible finite-volume LES with an explicit or lightly implicit convective treatment; 5 to 20 microseconds for an implicit solver doing several inner iterations per step; more again with combustion chemistry, Lagrangian particles or radiation. It is the only input here that cannot be derived from anything, and it enters the answer linearly, so a twenty-minute trial run on the real mesh and the real machine is worth more than any amount of care with the rest of the page.

Does DES really cost less than wall-modelled LES?

On this page’s model it does, and the reason is specific: DES runs the attached boundary layer in RANS mode, where the streamwise and spanwise cells can be anisotropic and much coarser than LES would allow, and only the separated focus region carries LES-quality spacing. Set the focus fraction to 1 and the DES estimate converges onto the wall-modelled LES one, which is the correct behaviour — if everything is separated there is no RANS region to economise in. The exponent on Reynolds number is the same for both, so DES is a constant-factor saving on top of wall-modelled LES rather than a change of scaling.

My Pope measure M comes out above 0.2. Is the run worthless?

No, but it is worth knowing. M above 0.2 means the subgrid model is supplying more than a fifth of the turbulent kinetic energy, which is more than Pope’s criterion allows for the label “LES”, and in practice a great deal of published wall-modelled LES sits between 0.2 and 0.4. The consequences are real: subgrid-model dependence goes up, the resolved spectrum rolls off early, and grid convergence in the LES sense becomes hard to demonstrate. Two cautions on the number itself. It assumes an inertial-range spectrum at the cutoff, which is optimistic near the spectral peak, and it depends on the integral length scale to the power minus two thirds — this page exposes that as an input for exactly that reason.

Why is the wall-normal cell count barely worth arguing about?

Because it enters the cell count linearly while the other two directions enter it as a product, and for a wall-modelled run the spanwise and streamwise spacing enter squared. Halving the wall-normal count saves a factor of two; relaxing the streamwise and spanwise cells per δ from 15 to 10 saves a factor of 2.25 and does so in the direction where the resolution requirement is set by resolving eddies rather than by resolving a mean profile. The wall-normal direction is also where the physics is least forgiving, since it carries the near-wall gradient that sets the shear stress.

How many flow-through times do I actually need?

Enough to flush the initial transient and then enough to average over, and the two are different questions. Two to three flow-through times will remove the initial condition from most external flows. After that, mean forces on an attached flow settle within about ten; a separated flow with large-scale unsteadiness may need thirty or more; second-order statistics need several times what the mean needs; and a spectrum needs a record long enough to resolve the lowest frequency you care about, which is a statement about time, not about flow-through times. The honest test is to split the sample in half and see whether the two halves agree.

Related calculators

References

H. Choi and P. Moin, Grid-point requirements for large eddy simulation: Chapman’s estimates revisited, Physics of Fluids 24 (2012), 011702. The source of the two exponents this page is built on: N proportional to Re_L^13/7 for wall-resolving LES, and the wall-modelled result, which the abstract states as Re_L^2/7 and which is linear in Re_L when the transition station is held at a fixed Reynolds number rather than at a fixed fraction of the body length. Also the source of the statement that wall modelling saves one to three orders of magnitude in grid points on aircraft-scale flows.
D. R. Chapman, Computational Aerodynamics Development and Outlook, AIAA Journal 17 (1979), 1293–1313. The original grid-point estimate, N proportional to Re_L^9/5, which the 2012 paper revises. Cited, not reproduced.
F. M. White, Viscous Fluid Flow. Source of the turbulent flat-plate correlations used here: c_f = 0.027 Re_x^−1/7, δ/x = 0.16 Re_x^−1/7 and θ/x = 0.016 Re_x^−1/7. The three are mutually consistent and were checked as such before use: the momentum-integral identity c_f/2 = dθ/dx holds between them to 1.6%, and θ/δ = 0.10 against the 7/72 = 0.0972 a one-seventh-power profile requires.
H. Schlichting and K. Gersten, Boundary-Layer Theory. Source of the logarithmic fit c_f = (2 log₁₀Re_x − 0.65)^−2.3, used here only as an independent check on the correlation above, and of the older one-fifth power law c_f = 0.0576 Re_x^−1/5 that underlies Chapman’s exponent. Cited, not reproduced.
S. B. Pope, Turbulent Flows, Cambridge University Press, 2000. Source of the resolution measure M — the fraction of turbulent kinetic energy in the residual motions — and of the criterion that M should be below about 0.2 for a simulation to count as a large-eddy simulation. Also the source of the Taylor microscale definition λ = √(15νu′²/ε) and of the Kolmogorov scaling relations used here. Cited, not reproduced.
Ansys, Ansys HPC Seminar 2021 — CFD presentation material (public copy hosted by CMC Microsystems). Source of the parallel-efficiency figures quoted in the notes: excellent efficiency above about 10,000 cells per core and good scaling down to about 2,500. Attributed to the named vendor rather than presented as a general law, because it is measurement on one solver.
X. I. A. Yang and K. P. Griffin, Grid-point and time-step requirements for direct numerical simulation and large-eddy simulation, Physics of Fluids 33 (2021), 015108. Restates the Choi and Moin exponents and adds time-step and total-cost scalings. Its total-cost figures differ from the ones derived here because it sets the time step from a different station in the boundary layer; the difference is a modelling choice about which cell the global time step is taken on, and both are stated on this page rather than one being quietly preferred.
Derivations performed for this page, not taken from a source (1): both cell-count integrals were evaluated in closed form from White’s correlations and then differentiated numerically. The local exponent d ln N/d ln Re_L converges to 1.85714 for the wall-resolved model and to 1.00000 for the wall-modelled model as Re_L/Re_x0 grows, reproducing 13/7 and 1 to five decimal places; setting Re_x0 proportional to Re_L instead gives 0.28571, reproducing 2/7 exactly. The same integral with one further power of u_τ/ν, which is the DNS case, gives 37/14 = 2.64286.
Derivations performed for this page, not taken from a source (2): Pope’s measure was evaluated as M = C_K(Δ/π&ell;)^2/3 with C_K = 1.5, ε = u′³/&ell; and a cutoff wavenumber π/Δ. The Kolmogorov and Taylor lengths the calculator reports were checked against the identities η/&ell; = Re_t^−3/4 and λ/η = √15 Re_t^1/4, which they satisfy to machine precision.

Setup guidance, not validation. Correlations have ranges of validity and cell-count estimates are order-of-magnitude. A converged simulation is not a correct one. Full disclaimer at calcengines.com/disclaimer/