Convective Time Scale and Simulation Timing

A large-eddy simulation does not “converge” to a single steady answer the way a RANS solver does. It produces a turbulent time signal, and the quality of every quantity you extract from that signal - a mean pressure, an RMS, a peak suction - depends on how long you let the flow run. The convective time scale is the natural clock for planning that duration.

This page defines the convective time scale (also called the flow-through time), explains why one simulation actually involves two such scales, and gives practical magnitude guidance for how many you need before means, fluctuations, and peaks are trustworthy.

See also

For non-dimensionalising a probe time series after the run - normalising by the eddy turnover time built from the integral length scale - see Time Normalization Using the Integral Length Scale.

Definition

The convective time scale (CTS), or flow-through time (FTT), is the time a fluid parcel takes to travel one characteristic length \(L\) at a representative velocity \(U\):

\[T = \frac{L}{U}\]

It answers a simple question: how long does it take the flow to convect information across a length of interest? Everything downstream - how long to wash out the initial field, how long to sample statistics - is naturally measured in multiples of \(T\), not in seconds. Working in convective time scales removes the dependence on the specific size of your domain and the specific wind speed, so the same guidance transfers across cases.

Note

Physical seconds are rarely the useful unit for planning a run. A 2 m/s pedestrian-comfort study and a 40 m/s cladding study can need a similar number of convective time scales, even though their durations in seconds differ by an order of magnitude.

The two scales: development vs statistics

The subtlety that comes up most often is that a single simulation has two convective time scales, because there are two length scales that matter:

  • Domain scale - \(L\) is the streamwise length of the computational domain. The corresponding flow-through time governs development: how long the flow takes to travel from the inlet, past the geometry, and out through the outlet, replacing the initial condition with fully developed turbulence.

  • Body scale - \(L\) is a characteristic length of the phenomenon you are measuring (typically the building height or width). The corresponding convective time governs statistics: how many times a structure of that size must be advected past your probes before the running mean, variance, and extremes settle.

The domain-scale flow-through time is large; you only need a couple of them. The body-scale convective time is small; you need hundreds of them. Confusing the two is the usual reason a run is either wastefully long or too short to trust.

Important

Development is measured in domain-scale flow-through times. Statistical convergence is measured in body-scale convective time scales. When this page quotes magnitudes like “300 CTS”, it refers to the body-scale convective time - the characteristic length of the geometry, not the length of the domain.

How many do you need?

The number of convective time scales required grows sharply with the statistical order of the quantity: a mean settles quickly, a variance more slowly, and an extreme value slowest of all, because rare events have to occur enough times to be sampled reliably.

The values below are typical planning targets, not hard thresholds. Verify convergence for your own case by checking that the running statistic has flattened (see Checking convergence in practice below).

Phase

Quantity

Typical convective time scales

Development

Wash out the initial field

~2 domain flow-through times

Sampling

Mean quantities (mean \(C_p\), mean velocity)

~300

Sampling

RMS / fluctuations (turbulence intensity, standard deviation)

~500-600

Sampling

Peaks (peak suction, peak overpressure)

~900+

Note

These are cumulative in effort, not additive to the same total: a run configured for reliable peak statistics (~900+ CTS) has, by construction, more than enough samples for the means and RMS extracted from the same signal.

Why peaks need the most

A mean averages every sample, so it converges roughly with the number of independent samples. An RMS depends on the spread of the fluctuations and needs enough turnover of the large eddies to see the full distribution. A peak depends on the tail of that distribution - the rare, large excursions that drive cladding and glazing design - and you simply have to run long enough for enough of those rare events to occur. This is why peak suction and peak overpressure set the total duration of a design run.

Reference velocity

The velocity \(U\) in \(T = L/U\) is a representative flow speed for the case. It also feeds the Reynolds matching and the inlet profile, so it is worth choosing deliberately.

  • Typical structural / cladding studies: 20-40 m/s.

  • Pedestrian comfort: 2-3 m/s at pedestrian height.

Tip

The reference velocity is an estimate at setup time. Once the run is going, the actual measured speed at your reference location may differ from the nominal inlet value; if it does, recompute the convective time scale from the measured velocity so your sampling-duration target stays honest.

Checking convergence in practice

Because LES has no residual to watch, convergence is judged from the statistics themselves rather than from a solver metric:

  • Plot the running mean and running RMS of a representative probe against convective time. When the curve has flattened and stopped drifting, that statistic has converged.

  • Higher-order statistics flatten later than lower-order ones - expect the mean to settle well before the RMS, and the RMS well before the peaks.

  • If a curve is still drifting at the end of the run, the sample is too short for that quantity; extend the run rather than trust the number.

See also

LES stability and live monitoring (max/mean/min velocity and pressure, spotting a pressure blow-up) are covered under Running a Simulation.

Relation to the solver time step

The convective time scale sets the total physical duration of the run. The solver’s internal time step \(\Delta t\) - how finely that duration is discretised - is a separate quantity, computed automatically from the CFL condition, the top velocity, and the grid spacing \(\Delta x\). Finer refinement levels advance more time steps per coarse step (see Computational Mesh), so the number of iterations behind a given number of convective time scales grows with refinement, even though the physical duration does not.

Note

Plan the run in convective time scales (physical duration); let the solver derive the time step and iteration count. You choose how long, the solver chooses how finely.

See also