Adaptive time stepping method

The thermal solver uses the adaptive time stepping method to automatically determine the time step sizes in a transient thermal simulation. This method handles the sharp changes in temperature at boundary conditions. When there are no abrupt changes in boundary conditions, it accelerates the simulation without losing accuracy. The time step size calculation is based on the estimated error between a quadratic fit and a linear fit of the solution in time.

When there are abrupt temperature changes in the model, as seen in the example, the adaptive time stepping scheme adapts by performing smaller time steps around the times when the abrupt changes occur. The blue curve represents the time-varying heat load that is applied to the boundary condition and each red + represents the temperature value at one point of the boundary condition for the transient run. The x’s that are close to each other indicate that the time steps are smaller at those times to better capture the changes in the heat load.

You specify the temperature error tolerance, the minimum time step size, and the maximum time step size.

Algorithm for the adaptive time stepping method

The estimated error, e, is the difference between a fit quadratic function and a linear variation through three consecutively computed temperature values (T0, T1, and T2) for two consecutive time steps (Δt0 and Δt1).

The time range for the complete transient simulation contains inflection points, represented by the red dots, that are time points where there is an abrupt change in boundary conditions. This includes the starting and ending times of the solution and of the solution steps if present.

• At an inflection point, the solver initializes the first two time steps, usually to a small value.

• After the initial two time steps are computed, if the estimated error is unacceptable, both time steps are reduced and the solution is recomputed for the first two time steps.

• After the initial two time steps are completed, the thermal solver computes subsequent time steps based on the error estimate.

• The solver continues to use the error estimates until a new inflection point is encountered or the end of the simulation is reached. If a new inflection point is encountered earlier than the projected time step, a smaller time step is used to reach that inflection point. The solver adjusts the time step while respecting the specified minimum time step for all inflection points except the end of a solution step or of the simulation. In these cases, the solver ignores the minimum time step criterion and uses a time step as small as necessary to reach the end times.

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