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  • Documentation

    How to Determine the Time Step Size for Transient Output in LBM Simulations?

    The Incompressible LBM solver offers three types of output fields for a simulation: Transient output, Statistical averaging, and Snapshot. From these three, the transient output is the only one that writes the fields as a function of time. As such, it is important to know the time step size that will be used in the transient output fields.

    animation for lbm transient output
    Animation 1: Transient flow field around a building.

    This value is controlled by two parameters, as found in the Transient output panel: Write control and Fraction from end:

    simscale lbm transient output setup panel time step size
    Figure 1: Setup panel for the transient output

    The Fraction from end determines the total period of time written, as a proportion of the End time under Simulation control. In the example given in Figure 1, the last 20% of the simulated time will be written.

    On the other hand, the Write control determines the time step size. If set to Manual, the step size can be input directly. If an automatic resolution is used, then the step size is computed as a proportion of the simulation time step.

    Computing the Automatic Time Step Size

    The automatic time step size in the transient output is computed using the following equation:

    $$ \Delta t_{out} = \Delta t_{sim, max} \cdot c_{res} \tag{1} $$


    • \( \Delta t_{sim, max} \) is the maximum time step size used in the simulation, computed as shown below.
    • \( \Delta t_{out} \) is the time step size of the transient output
    • \( c_{res} \) is the resolution coefficient, given in table 1:
    Write ControlResolution Coefficient
    Coarse resolution8
    Moderate resolution4
    High resolution2
    Table 1: Values for the resolution coefficient

    The simulation time step size is computed as a function of the mesh size:

    $$ \Delta t_{sim} = \frac{ h }{ 10 U_{ref} } \tag{2} $$


    • \( h \) is the minimum or maximum cell size
    • \( U_{ref} \) is the reference flow speed, as applied at the inlet face

    It is important to notice that the solver determines a minimum and a maximum time step, based on the corresponding cell sizes. For the transient output, the maximum time step is used as a base for the computation of the output step size.

    Determining the Cell Size

    The cell size is a function of the reference length and the fineness specified under mesh settings. For Automatic meshing:

    simscale lbm mesh settings
    Figure 2: Setup panel for mesh settings

    $$ h_{max} = \frac{ L_{ref} }{ n } \tag{3} $$

    $$ h_{min} = \frac{ h_{max} }{ 2^{m} } \tag{4} $$


    • \( L_{ref} \) is the reference length value specified in the mesh settings or automatically computed
    • \( n \) is the number of cells per length
    • \( m \) is the number of refinement levels

    \(n\) and \(m\) are defined from the Fineness parameter according to Table 2:

    FinenessNumber of Cells
    per Length, \(n\)
    Number of
    Refinement Levels, \(m\)
    Very coarse164
    Very fine246
    Table 2: Number of cells per length from the mesh fineness

    Example Computation

    To demonstrate the computation, let’s assume a case with the following parameters:

    • Reference length \( L_{ref} = 200\ m \)
    • Inlet velocity \( U_{ref} = 10\ m/s \)
    • Mesh fineness is Coarse
    • Write control under Transient output has Coarse resolution

    Then we proceed to the computation:

    From table 2, the number of cells per length \( n = 16 \) and the number of refinement levels \( m = 5 \)

    The maximum cell size is computed from equation 3:

    $$ h_{max} = \frac{ 200\ m }{ 16 } = 12.5\ m $$

    And the minimum cell size from equation 4:

    $$ h_{min} = \frac{ 12.5\ m }{ 2^5 } = 0.391\ m $$

    The time step size range for the simulation will be:

    $$ \Delta t_{sim, min} = \frac{ 0.391\ m }{ 10 (10\ m/s) } = 3.91\ ms $$

    $$ \Delta t_{sim, max} = \frac{ 12.5\ m }{ 10 (10\ m/s) } = 0.125\ s $$

    From table 1, the resolution coefficient is \( c_{res} = 8 \)

    Finally the output time step is computed from the maximum time step size:

    $$ \Delta t_{out} = (0.125\ s)(8) = 1\ s $$


    If none of the above suggestions solved your problem, then please post the issue on our forum or contact us.

    Last updated: December 28th, 2021