Chapter 9

Question 1

What is the upper limit for time step choice?

Answer 1

When the time step is larger than 1/10 of the time coefficient.

Question 2

What is time-step convergence?

Answer 2

Time step convergence is a practical way to assess the optimal time step of integration (delta t) for the numerical solution of a model.

Time step convergence is based on the ratio between the time step of integration and the characteristic time (TC or tau) of the model.

Question 3

What is the equation that describes time-step convergence?

Answer 3

delta t / TC

Question 4

Why is time-step convergence useful?

Answer 4

1. easy understanding of model equations
2. model integrity with respect to its units is maintained
3. the best numerical value of the time step for the model can be easily assessed by means of time step convergence

Question 5

What happens if an explicit time step is NOT present?

Answer 5

If delta T is not present model unit integrity can only be satisfied if the value of unity (1) is assumed as the time step of integration.

the ratio between the time step of integration and the characteristic time of the model (now 1/TC) can only be changed if TC is changed.

Question 6

Why might one expect a converging model outcome when implementing a specific numerical integration technique, and what action could be taken to achieve this result?

Answer 6

Gradually decreasing time step should produce a converging model outcome.