# Time Stepping

# Is the simulation steady?

A steady simulation attempts to converge to a steady-state flow solution. Answer no for an unsteady simulation that solves for unsteady flow physics. For the latter, you will need to enter a physical time step size and the total number of time steps.

# Time step size for unsteady simulation (seconds)

A second-order implicit time stepping scheme will be used to converge each time step. Enter here the physical time step size, . Note that this time step size will be nondimensionalized using the freestream speed of sound and the mesh length unit when generating timeStepSize for the solver input JSON file.

timeStepSize

For steady simulations, the physical time step size is equivalent to inf, and only one physical time step is needed.

# How many time steps do you want to simulate?

A second-order implicit time stepping scheme will be used to converge each time step. Enter number of time steps here. Note that nonlinear iterations will be used to converge each time step. You will need to enter the number of nonlinear iterations in the next field.

# The maximum number of nonlinear iterations used to converge each physical time step

A nonlinear iteration scheme (quasi-Newton) will be used to converge each physical time step. When the maximum number of iterations is reached, the solver will proceed to the next physical time step, even if the final nonlinear residuals are still higher than the tolerance.

# Initial CFL number

Flow360 uses a dual time stepping strategy.

For unsteady simulations, nonlinear iterations through pseudo-time steps are used to converge flow solutions within each physical time step. The CFL number is used by the solver to determine the pseudo time step size. As a measure of numerical stability, the CFL number may be regarded as that it controls how aggressive each pseudo-time iteration is. An iteration with a smaller CFL number makes less progress towards convergence, but is safer from divergence. An iteration with a larger CFL number makes more progress but could lead to divergence before flow solutions converge. Therefore, we recommend starting from a small (safe) initial CFL number of around 1, and ramping it up towards a larger final value of 100 or higher.

For steady simulations, the settings for the CFL number are the same as above.

# Final CFL number

see initial CFL number

# CFL ramping steps

During each non-linear iteration, the CFL number will ramp up from the initial to the final value during this number of CFL ramping steps. If the maximum number of nonlinear iterations is lower than this number of ramping steps, the final CFL value will be never reached. If the maximum number of nonlinear iterations is larger than this number of ramping steps, the final CFL value will be reached and used for the rest of the iterations. See the initial CFL number for more details.