A general CFD framework for fault-resilient simulations based on multi-resolution information fusion

Seungjoon Lee, Ioannis G. Kevrekidis, George Em Karniadakis

Research output: Contribution to journalArticlepeer-review

11 Scopus citations


We develop a general CFD framework for multi-resolution simulations to target multiscale problems but also resilience in exascale simulations, where faulty processors may lead to gappy, in space-time, simulated fields. We combine approximation theory and domain decomposition together with statistical learning techniques, e.g. coKriging, to estimate boundary conditions and minimize communications by performing independent parallel runs. To demonstrate this new simulation approach, we consider two benchmark problems. First, we solve the heat equation (a) on a small number of spatial “patches” distributed across the domain, simulated by finite differences at fine resolution and (b) on the entire domain simulated at very low resolution, thus fusing multi-resolution models to obtain the final answer. Second, we simulate the flow in a lid-driven cavity in an analogous fashion, by fusing finite difference solutions obtained with fine and low resolution assuming gappy data sets. We investigate the influence of various parameters for this framework, including the correlation kernel, the size of a buffer employed in estimating boundary conditions, the coarseness of the resolution of auxiliary data, and the communication frequency across different patches in fusing the information at different resolution levels. In addition to its robustness and resilience, the new framework can be employed to generalize previous multiscale approaches involving heterogeneous discretizations or even fundamentally different flow descriptions, e.g. in continuum-atomistic simulations.

Original languageEnglish (US)
Pages (from-to)290-304
Number of pages15
JournalJournal of Computational Physics
StatePublished - Oct 15 2017

All Science Journal Classification (ASJC) codes

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


  • Domain decomposition
  • Exascale computing
  • Gap-tooth algorithm
  • Gappy data
  • Machine learning
  • Multi-resolution simulation
  • Resilience
  • coKriging


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