The present tutorial example aimed at showing the different strategies to be used in combination for achieving a smooth-steady state solution when using an explicit solver for dynamic problems. The key points are summarised as follows:

 

 

•The target is to minimize dynamics/oscillation in the solution. In order to achieve that three strategies are usually applied in combination in geomechanical simulations:

 

oUse enough mechanical time steps to solve the loads applied at each simulation stage. In this way the increment in load for each mechanical time step will be sufficiently low so that the resulting inertia effects will be relatively small. This is achieved by defining either the Target_number_time_steps in Control_data or defining the target time step size via Optimal_time_step keyword within Time_scaling_factors data structure. In both cases the code will automatically apply the corresponding mass-scaling required for each group in the simulation. Note that definition of Factor_critical_time_step < 1.0 in Control_data is also required (recommended default values are 0.9 in 2D problems and 0.7 in 3D problems).

 

oThe required number of time steps per simulation stage/load application is case dependent and depends on several factors (e.g. magnitude of the load applied, stiffness of materials, etc.). Nonetheless a good starting point is to use at least 10000 time steps per stage. For simulations coupling the mechanical and flow fields the number of mechanical steps per flow steps is also relevant to ensure stability. A minimum of 100 mechanical steps per flow step is recommended (but more may be required).

 

oApply damping in the solution via Damping_global_data data structure. Different damping models may be applied:

 

•Low frequency damping (mass proportional damping) via Percentage_damping keyword with a recommended default value of 0.02.

 

•High frequency damping via Bulk_damping_model keyword with definition of the BulkViscosity model with a recommended default value of 0.5 for the bulk viscosity constant.

 

oApply the loads using S-shaped time functions via definition of Curve_type 2 in Time_curve_data data structure. In this way the loading rate at the beginning and end of the load application will tend to zero hence minimizing the inertia effects. There is an exception to this rule and this is when modelling deposition of sediments on salt (i.e. mini-basins). Salt is very mobile and sometimes reacts as a fluid to the loads applied. Therefore a series of sediment formations deposited using S-shaped curves for gravity initialization may result in the creation of "waves" within the salt due to the intermittent high loading rate (middle of deposition of a formation) / low loading rate (beginning/end of formation deposition) regimes.

 

 

•The remaining dynamics/oscillations in the solution may be monitored in ParaGeo by:

 

oUsing high frequency output in History_point at selected point locations and request output of velocity and stresses for example. Velocity should be negligible at the end of a load application (usually at the end of each simulation stage).

 

oAlternatively kinetic energy may be monitored using History_global and compare it to elastic energy. Kinetic energy must be much lower than the elastic energy (3 orders of magnitude or more).