Multirate timestepping for the incompressible Navier-Stokes equations in overlapping grids

Ketan Mittal, Som Dutta, Paul Fischer

Research output: Contribution to journalArticlepeer-review


We develop a multirate timestepper for semi-implicit solutions of the unsteady incompressible Navier-Stokes equations (INSE) based on a recently-developed multidomain spectral element method (SEM) [1]. For incompressible flows, multirate timestepping (MTS) is particularly challenging because of the tight coupling implied by the incompressibility constraint, which manifests as an elliptic subproblem for the pressure at each timestep. The novelty of our approach stems from the development of a stable overlapping Schwarz method applied directly to the Navier-Stokes equations, rather than to the convective, viscous, and pressure substeps that are at the heart of most INSE solvers. Our MTS approach is based on a predictor-corrector (PC) strategy that preserves the temporal convergence of the underlying semi-implicit timestepper. We present numerical results demonstrating that this approach scales to an arbitrary number of overlapping grids, accurately models complex turbulent flow phenomenon, and improves computational efficiency in comparison to singlerate timestepping-based calculations.

Original languageEnglish (US)
Article number110335
JournalJournal of Computational Physics
StatePublished - Jul 15 2021


  • High-order
  • Multirate
  • Navier-Stokes
  • Nonconforming
  • Overset

ASJC Scopus subject areas

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


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