17.4.3. Solution Algorithm

While film movement is always tracked with time, the EWF model can be run with both steady and transient flow simulations.

17.4.3.1. Steady Flow

It is assumed that while flow affects its movement, the thin film does not, however, affect the flow field. In this case the flow field has converged and is kept unchanged (frozen flow field). The elapsed time for film development is increased by the film time step, . This time step can either be a user-specified constant or can be computed automatically using an adaptive time-stepping method with user-specified increase and decrease factors, depending upon the maximum Courant number, described as follows:

  • When the computed maximum Courant number exceeds the user-specified value, the film time step is reduced by a decrease factor (default: 2).

  • When the computed maximum Courant number is less than half of the user-specified value, the film time step is increased by an increase factor (default: 1.5).

17.4.3.2. Transient Flow

Within each flow time step, , a number of film sub-time steps are used to advance the film time to the same physical time of flow. The film sub-time step is determined as follows,

(17–52)

is the number of film time steps; is the flow time step.

Adaptive time stepping is achieved by adjusting the number of film time steps using user-specified increase and decrease factors and :

  • When the computed maximum Courant number exceeds the user-specified value, the number of film time steps is increased by a factor of , hence reducing the film time step by factor .

  • When the computed maximum Courant number is less than half of the user-specified value, the number of film time steps is reduced by a factor of , hence increasing the film time step by factor .

    Note that the minimum number of film time steps that can be reduced to is 2.

Since film computation starts at the end of each flow time step, the effect of the film on flow is lagged by one flow time step.