@article{10812,
  author = {Omar Al-Khayat and Hans Langtangen},
  title = {Computational Aspects of Multiscale Simulation With the Lumped Particle Framework},
  abstract = {First introduced in [2], the lumped particle framework is a flexible and numerically efficient framework for the modelling of particle transport in fluid flow. In this paper, the frame- work is expanded to simulate multicomponent particle-laden fluid flow. This is accomplished by introducing simulation protocols to model particles over a wide range of length and time scales. Consequently, we present a time ordering scheme and an approximate approach for ac- celerating the computation of evolution of different particle constituents with large differences in physical scales. We apply the extended framework on the temporal evolution of three parti- cle constituents in sand-laden flow, and horizontal release of spherical particles. Furthermore, we evaluate the numerical error of the lumped particle model. In this context, we discuss the Velocity-Verlet numerical scheme, and show how to apply this to solving Newton{\textquoteright}s equations within the framework. We show that the increased accuracy of the Velocity-Verlet scheme is not lost when applied to the lumped particle framework.},
  year = {2012},
  journal = {Communications in Computational Physics},
  volume = {12},
  number = {4},
  pages = {1257-1274},
}