Time scaling

Time scaling

 

Description

 

Here the *TIME SCALING keyword and its corresponding parameters are described. This is used to automatically adjust the element mass in the explicit geomechanical solver to optimise the time step in quasi-static problems. The algorithm is based on a user specified target time step together with a maximum allowable increase/decrease in the mass. It is an alternative/complementary approach to the material based mass-scaling to reduce inertia effects and optimize the time step. Note that a method to automatically compute the appropriate mass scaling for all elements in the domain to achieve an specified "optimal" time step is available and is recommended (*TIME SCALING, TYPE=Optimal).

 

Time step in ParaGeo

In order to achieve a quasi-static solution for a mechanical analysis using explicit dynamic solvers the increment in load between consecutive time steps should be sufficiently small to minimize inertia effects (for a given load, time step should be sufficiently small). In ParaGeo the time step used for simulation is calculated in such a way so it is below the critical time step (time step above which the solution may be unstable) by introducing a critical step factor so that:

Time_step

 

And the critical time step is evaluated as:

 

Critical_time_step

 

Therefore, in order to use a larger number of time steps and thus minimize the inertia effects the critical time step should be decreased via mass-scaling (decreasing the mass results an increase in the element wave speed what in turn decreases the critical time step). However not all elements have the same critical time step as it also depends on the element length and in addition, groups with different material properties may have different Young's modulus. Therefore the time scaling is used to define a target / optimal time step and increase the mass (already down scaled) for such elements that satisfy Time_scaling_condition so that Time_scaling_condition2 (time scaling equalizes the critical time step).

 

 

TIME SCALING    Mechanical Time Step data

Usage

*TIME SCALING,  TYPE=OPTIMAL,  TARGET TIME=Value,  TARGET STEPS=Value

Description

Defines data to set the mechanical time step. It generates Time_scaling_factors data in ParaGeo.

 

Optional Parameters

TYPE

Selects the model used for defining the mechanical time step. In ParaGeo three models are available:

- UPPER TARGET

Mass can only be scaled up (increase) by time scaling

- ABSOLUTE

Mass can either be increased or decreased by time scaling

- OPTIMAL (Default)

Mass can either be increased or decreased by time scaling. Initial mass scaling is not required.

TARGET TIME

Defines the target mechanical time step size for the simulation. When the model "Optimal" is used, the mass is scaled for all elements in the domain so that the critical time step is approximately equal to the input TARGET TIME for all groups. If not defined *TARGET STEPS must be defined instead.

TARGET STEPS

The time step size can optionally be input as the target number of mechanical steps for a given simulation Stage/Step. The data however is converted as target time step for ParaGeo input as: DurationSTAGE / NStepsTARGET. If not defined *TARGET TIME must be defined instead.

 

 

Examples

 

*TIME SCALING, TYPE=OPTIMAL, TARGET TIME=1E-4

 

 

1The optimal time step model will be used for time scaling with an optimal target time step of 0.0001 years (model units).