Realizable ODE solver

Settings for the realizable ODE solver

The integration of source terms in the moment evolution equation may lead to unrealizable moment sets, and put an excessively strict constraint on the time-step of the simulation. In order to address this concern, the realizable ODE solver of Nguyen et al. (T.T. Nguyen, F. Laurent, R.O. Fox, M. Massot, Solution of population balance equations in applications with fine particles: Mathematical modeling and numerical schemes, Journal of Computational Physics. 325 (2016) 129–156. doi:10.1016/ has been implemented. The integrator is based on a predictor-corrector Runge-Kutta scheme with adaptive integration step deterrmined by ensuring the accuracy of teh solution within the specified tolerance and the realizability of the moment vector.

This ODE solver requires a set of parameters to be specified:

  • Atol: absolute tolerance
  • RTol: relative tolerance
  • fac: time-step change factor
  • facMin: minimum value of the time-step change factor
  • facMax: maximum value of the time-step change factor
  • minLocalDt: minimum value of the time-step used in the ODE solver

These parameters are specified in the odeCoeffs sub-dictionary for the corresponding model (mixing, population balance, …):

    ATol       1.0e-8;
    RTol       1.0e-4;
    fac        0.9;
    facMin     0.5;
    facMax     2.0;
    minLocalDt 1.0e-5;

The implementation details of the realizable ODE solver are visible in the source code on GitHub.