Time-step coupling for hybrid simulations of multiscale flows

Duncan A. Lockerby*, Carlos A. Duque-Daza, Matthew K. Borg, Jason M. Reese

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract / Description of output

A new method is presented for the exploitation of time-scale separation in hybrid continuum-molecular models of multiscale flows. Our method is a generalisation of existing approaches, and is evaluated in terms of computational efficiency and physical/numerical error. Comparison with existing schemes demonstrates comparable, or much improved, physical accuracy, at comparable, or far greater, efficiency (in terms of the number of time-step operations required to cover the same physical time). A leapfrog coupling is proposed between the 'macro' and 'micro' components of the hybrid model and demonstrates potential for improved numerical accuracy over a standard simultaneous approach. A general algorithm for a coupled time step is presented. Three test cases are considered where the degree of time-scale separation naturally varies during the course of the simulation. First, the step response of a second-order system composed of two linearly-coupled ODEs. Second, a micro-jet actuator combining a kinetic treatment in a small flow region where rarefaction is important with a simple ODE enforcing mass conservation in a much larger spatial region. Finally, the transient start-up flow of a journal bearing with a cylindrical rarefied gas layer. Our new time-stepping method consistently demonstrates as good as or better performance than existing schemes. This superior overall performance is due to an adaptability inherent in the method, which allows the most-desirable aspects of existing schemes to be applied only in the appropriate conditions.

Original languageEnglish
Pages (from-to)344-365
Number of pages22
JournalJournal of Computational Physics
Publication statusPublished - 15 Mar 2013

Keywords / Materials (for Non-textual outputs)

  • multiscale simulations
  • unsteady micro/nano flows
  • hybrid methods
  • scale separation
  • microjet actuators
  • heterogeneous methods
  • time scale separation
  • coupling
  • rarefied gas dynamics
  • journal bearing
  • adaptive time-stepping
  • domain decomposition


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