flowfield CFD REFERENCE
Equations and turbulence

How much flow can you resolve?

Compare seven approaches by what their equations represent, what they resolve and where the compute goes.

Relative compute effort

Indicative bands for comparable turbulent external-aerodynamics questions. Mesh size, time step, run duration and hardware determine actual cost.

  1. Euler
    Low

    An inviscid grid skips the viscous boundary layer.

  2. Steady RANS
    Low to moderate

    Converges a steady mean. Wall spacing still matters.

  3. URANS
    Moderate to high

    Advances through physical time to follow changing loads.

  4. DES / DDES / IDDES
    High to very high

    Needs a 3D transient grid fine enough to resolve the wake.

  5. Wall-modeled LES
    High to very high

    Resolves outer eddies with coarser near-wall spacing than wall-resolved LES.

  6. Wall-resolved LES
    Very high to extreme

    Fine spacing along and across walls drives up cell and time-step counts.

  7. DNS
    Extreme

    The grid and time step resolve the smallest relevant turbulent scales.

The bands are qualitative and can overlap. A steady RANS solution can be cheaper than DNS even though its turbulence model adds equations. DNS spends its compute resolving the flow over finer scales.

What one aircraft case took to run

A high-lift aircraft study compared SA-based runs on the JAXA JSS3 supercomputer. Its published compute estimates include the solver and file I/O.

  • Steady RANS32,000 core-hours 576 cores
  • URANS300,000 core-hours 576 cores
  • DDES320,000 core-hours 1,920 cores

One core-hour is one core running for an hour. The steady run budget is for 200,000 iterations. The unsteady budgets cover 72.5 convective time units each. The runs used different grids or time steps, so these numbers describe this study’s setup. Source · Table 9 and Table 10

Which motions does each approach see?

Conceptual views of a turbulent flow above a wall.

RANSThe closure represents the effects of turbulent fluctuations on the mean.
Hybrid RANS–LESIn a typical separated-flow setup, the wall layer is modeled and larger wake motions are resolved.
LESThe filter sets the scale separation. A closure accounts for smaller motions.

Green shows the flow or motions represented directly. Shaded regions and dashed marks indicate modeled turbulence.

What changes in the equations?

Euler
Mass, momentum and energy with inviscid fluxes.Pressure loads and shocks where viscous effects can be neglected.
Steady RANS
Averaged flow equations with a closure such as SA or SST.Cruise loads and early design sweeps.
URANS
Time-dependent averaged equations with a RANS closure.Forced motion or periodic loads that the closure can capture.
DES / DDES / IDDES
A grid-aware closure changes where turbulence is modeled and where it is resolved.Separated flows and unsteady loads.
Wall-modeled LES
Filtered flow equations, a subgrid closure and a wall model.Scale-resolving aircraft and separated-flow research.
Wall-resolved LES
Filtered flow equations with a subgrid closure. Near-wall motions are resolved.Detailed flow physics when the Reynolds number and budget allow it.
DNS
The unaveraged equations, without a turbulence closure.Research and benchmark flows, usually at smaller scales than a full aircraft.