Prior Transient Integration

Determining the initial conditions for the implicit variables Prior Transient Integration and Extended Prior Transient Integration... 

However, an option more in keeping with the Method of Referred Derivatives is that of Prior Transient Integration . At an assumed time, tp r, prior to the transient start time, we select an artificial set of states, x(t/,rmr)f and inputs, u(tp,jer), chosen solely on the basis that they enable a direct (i.e. non-iterative) solution for the variables z to be found at time tprwr from ... 

Generating the starting conditions using Prior Transient Integration... 

The pressure derivatives found from equation (18.50) for Prior Transient Integration and (18.54) for Extended Prior Transient Integration were integrated using the Euler method. In each case the error was measured in terms of the sum of the squared flow errors, E, at time to ... 

The initial condition may be determined by an iterative solution of equation (2.93) just once at the beginning of the simulation, or, indeed, by a prior, off-line calculation. Alternative techniques based on integrating an artificial prior transient are given in Chapter 18, Sections 18.7 to 18.9, where a more detailed worked example is given. 

The expressions for transient concentration derived in the preceding section needs integration prior to use. More easily usable expressions can be developed by making suitable approximations. Realizing that for PDE, a set of functions instead of constants, as in the case of ODE, needs to be solved from the boundary condition Equation (9.96) is allowed to vary with time. This results in an expression for transient concentration that is more readily available for direct use of the practitioner. Extension to three dimensions in space is also straightforward with this method. 

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