Time stepping

There are several ways that the inputs are used to determine the time step of particle-only, fluid-only, and coupled fluid-particle systems.

Fluid-only simulations

In fluid-only simulations, setting mfix.fixed_dt causes the fluid to advance with a fixed (constant) time step. If mfix.fixed_dt is not defined, then an appropriate time step is computed based on the advective CFL condition.

Caution

The adaptive time step based on the advective CFL condition is always computed and is strongly recommended for most cases.

• For a fixed time step simiulation, if the computed step size is smaller than mfix.fixed_dt for a fixed, the simulation aborts with the message:

  amrex::Abort::0::"Fixed dt is too large for fluid solve !!!
  

• For simulations using the adaptive time step:

  • If the computed time step is larger than mfix.dt_max, then the time step is set to dt_max

  • If the computed time step is smaller than mfix.dt_min, then the simulation aborts with the message:

    amrex::Abort::0::"Current dt is smaller than dt_min !!!
    

Particle-only DEM simulations

In particle-only DEM simulations, the time step used to advance particles, dtsolid, is determined by computing the collision time tcoll from particle properties, then dividing the result by the number of steps per collision, tcoll_ratio:

dtsolid = tcoll / tcoll_ratio;

Note

mfix.fixed_dt must be defined for particle-only DEM simulations, however it is only used to determine the frequency of outputs and has no effect on the particle advance. If a positive value is not specified for mfix.fixed_dt, then the code aborts with the following message:

amrex::abort::0::if running particle-only must specify fixed_dt in the inputs file !!!

Coupled fluid-DEM simulations

In a coupled fluid-DEM simulation, the fluid time step, dt, and the particle time step, dtsolid, are computed the same as in fluid-only and DEM-only simulations, respectively. If dt < dtsolid, then the particle sub-time step, subdt, is set to the fluid time step and one particle advance is taken. However, if dt > dtsolid (which is usually the case), then the number of sub-steps needed for DEM particles to advance the same total time as the fluid, nsubsteps, is computed by dividing dt by dtsolid and the particle sub-time step is computed by dividing dt by nsubsteps.

int nsubsteps = 1;
amrex::Real subdt = dt;

if (dt > dtsolid) {
 nsubsteps = amrex::Math::ceil(dt / dtsolid);
 subdt = dt / nsubsteps;
}

The following inputs are defined using the mfix prefix.

Key	Description	Type	Default
max_step	Maximum number of time steps to take	Int	-1
stop_time	Maximum time to reach (s)	Real	-1.0
fixed_dt	Flag to use a fixed time step	Int	0
cfl	CFL constraint (dt < cfl * dx / u) Defaults to 0.5 if mfix.advection_type = MOL Defaults to 0.9 if mfix.advection_type = Godunov ignored if mfix.fixed_dt = 1	Real	See note
dt_min	Abort if dt gets smaller than this value	Real	1.e-6
dt_max	Maximum value of dt if fixed_dt is not 1	Real	1.e14
tcoll_ratio	DEM time step equals the min collision time divided by this value	Real	50.0
walltime_limit	Runtime limit specified with format HH:MM:SS. When the runtime has almost reached the limit (approaching is computed by considering the average runtime needed for each step) then the simulation ends and a clean exit is performed	String	“”
clean_exit	This input represents the name of a file that, if found in the run folder, makes the code stop and perform a clean exit	String	“”

In the case of unsteady flow, the simulation will stop when either the number of steps reaches max_step or time reaches stop_time.

The following inputs are defined using the mfix prefix and are only relevant if running a steady state simulation.

Key	Description	Type	Default
steady_state	Are we running a steady-state calculation?	Int	0
steady_state_tol	Tolerance for checking if we have reached steady state (Must be set if steady_state = 1)	Real	None
steady_state_maxiter	Maximum number of allowed iterations to converge to steady state	Int	100000000