timeStepping
Contents
8.2.1. timeStepping#
8.2.1.1. timeStepSize
#
timeStepSize
prescribes the size of each physical time step.
For steady case, there is only one physical time step with timeStepSize
= \(\infty\).
For unsteady cases, there are two typical ways for determining the timeStepSize
:
Based on an expected vortex shedding frequency
Based on the desired angle of rotation per step
8.2.1.1.1. Vortex Shedding Frequency#
The vortex shedding frequency can be estimated by:
where \(U_\infty\) is the freestream speed, \(D\) is the characteristic length, for example the mean aerodynamic chord, and \(St\) is the Strouhal Number. An approximation of \(St = 0.2\) is typically appropriate for most CFD applications.
Typically, the physical time step size \(\Delta t\) is set as:
Note that the nondimensional timeStepSize
in Flow360.json should be:
Here is an example showing how to convert the physical time step size to nondimensional timeStepSize
.
8.2.1.1.2. Angle of Rotation per Step#
If there is a transient BET Line or a sliding interface modeled, then the timeStepSize
can be calculated from the desired angle of rotation in each physical step.
Scenario 
Angle per 

Transient BETDisks (i.e., BET Line) 
6 deg/step 
Rotor in sliding interface, phaseI:
Initializing the flowfield with 1storder solver

6 deg/step 
Rotor in sliding interface, phaseII:
Initializing the flowfield with 2ndorder solver

6 deg/step 
Rotor in sliding interface, phaseIII:
Collecting the data with 2ndorder solver

3 deg/step 
Strong bladevortex interaction (hover/descent) 
12 deg/step 
Generating highquality timeresolved animation 
0.51 deg/step 
For more information about 1st versus 2nd order solution, see orderOfAccuracy.
Once the angle per step is determined, then the timeStepSize
can be calculated:
where \(\theta\) is the angle of rotation in degrees. Note that the omegaRadians
here is the nondimensional rotation speed,
which can be easily converted from RPM.
8.2.1.2. maxPseudoSteps
#
For steady cases,
maxPseudoSteps
is typically 5K~10K. If the nonlinear residuals and/or the forces and moments are still changing, the user can always fork the completed case and let it run more pseudo steps.For unsteady timeaccurate cases,
maxPseudoSteps
is typically slightly larger thanrampSteps
so thefinal
CFL can be achieved. As shown in the examples below, whenrampSteps
= 10 thenmaxPseudoSteps
should be set to 12. IframpSteps
= 33 thenmaxPseudoSteps
should be set to 35.
 Example
timeStepping
for the 1storder unsteady cases "maxPseudoSteps" : 12, "CFL" : { "initial" : 1, "final" : 1000, "rampSteps" : 10 }
 Example
timeStepping
for the 2ndorder unsteady cases "maxPseudoSteps" : 35, "CFL" : { "initial" : 1, "final" : 1e+7, "rampSteps" : 33 }
For more information about 1st versus 2nd order solution, see orderOfAccuracy. The CFL number will be discussed in the following subsection.
8.2.1.3. CFL
#
The CFL number determines the pseudo step size in each physical step. The table below shows how to ramp up the CFL number for steady and unsteady cases.
Example 
Type 




Simple wing or fuselage, mostly attached linear flow 
Steady 
5 
200 
100 
Full aircraft with nonlinear flow, some separation, simple actuator/BET disks 
Steady 
1 
100~150 
1K~2K 
Full aircraft near onset of stall, largescale separation, challenging actuator/BET disks 
Steady 
0.1~1 
10~50 
3K~5K 
Forked/child case 
Steady 
parent 
parent 
1 
Rotor in sliding interface, 1storder solver 
Unsteady 
1 
1000 
~10 
Rotor in sliding interface, 2ndorder solver 
Unsteady 
1 
1e+5~1e+7 
30~50 
For steady cases,
initial
CFL < 1,final
CFL < 100,rampSteps
> 3K are considered as conservative. Such conservative values are only recommended for challenging cases.For unsteady cases, it is typically recommended to let the nonlinear residuals drop 2~3 orders of magnitude in each physical step. That is why higher
final
CFL and more aggressive CFL ramping values are suggested.For unsteady cases running 2ndorder solver,
final
CFL < 1e+5,rampSteps
> 50 are considered as conservative. DecreasingrampSteps
andmaxPseudoSteps
within each physical step will decrease the overall cost and runtime. For more information about 1st versus 2nd order solutions, see orderOfAccuracy.