About the Time Discrete Solver
The Time Discrete Solver is used to solve fluid dynamics problems using a projection method. Also, you can use the time-discrete solver to solve problems that have been discretized in time using the prev or bdf operator.
In the time-discrete solver you cannot use the d operator to get the time derivatives. That is why the prev operator is needed so that time derivatives can be written using the backward Euler method. However, the prev operator does not make it possible to define variables like this:
a=f(prev(a))
That is, you cannot use the time-discrete solver to solve incremental problems in time because a variable cannot be expressed in terms of itself. Such a formulation leads to a circular variable dependency. If you want to implement a variable that is dependent on itself, that variable must be a dependent variable that you solve for as a continuous ODE or PDE.
The time-discrete solver is not intended for solving general time-dependent structural mechanics problems. What is obtained with the time-discrete solver is a quasi-stationary approach; the inertial terms are not included. Also, it is more correct to compare the results using the time-discrete solver with those using the generalized-α solver with manual time stepping because for both of these solvers, no error checking is done for the local time error.
TimeDiscrete in the COMSOL Multiphysics Programming Reference Manual.