Multi-rate time integration on overset meshes

Research output: Contribution to journalArticlepeer-review


Overset meshes are an effective tool for the computational fluid dynamic simulation of problems with complex geometries or multiscale spatio-temporal features. When the maximum allowable timestep on one or more meshes is significantly smaller than on the remaining meshes, standard explicit time integrators impose inefficiencies for time-accurate calculations by requiring that all meshes advance with the smallest timestep. With the targeted use of multi-rate time integrators, separate meshes can be time-marched at independent rates to avoid wasteful computation while maintaining accuracy and stability. This work applies time-explicit multi-rate integrators to the simulation of the compressible Navier-Stokes equations discretized on overset meshes using summation-by-parts (SBP) operators and simultaneous approximation term (SAT) boundary conditions. We introduce a class of multi-rate Adams-Bashforth (MRAB) schemes that offer significant stability improvements and computational efficiencies for SBP-SAT methods. We present numerical results that confirm the efficacy of MRAB integrators, outline a number of implementation challenges, and demonstrate a reduction in computational cost enabled by MRAB. We also investigate the use of our method in the setting of a large-scale distributed-memory parallel implementation where we discuss concerns involving load balancing and communication efficiency.

Original languageEnglish (US)
Pages (from-to)325-346
Number of pages22
JournalJournal of Computational Physics
StatePublished - Nov 1 2019
Externally publishedYes


  • Adams-Bashforth
  • Chimera
  • Multi-rate time integration
  • Overset meshes
  • Simultaneous-approximation-term
  • Summation-by-parts

ASJC Scopus subject areas

  • Numerical Analysis
  • Modeling and Simulation
  • Physics and Astronomy (miscellaneous)
  • General Physics and Astronomy
  • Computer Science Applications
  • Computational Mathematics
  • Applied Mathematics


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