Computational modeling for high-fidelity coarsening of shallow water equations based on subgrid data

Sagy R. Ephrati, Erwin Luesink, Golo Wimmer, Paolo Cifani, Bernard J. Geurts

Research output: Contribution to journalArticleAcademicpeer-review


Small-scale features of shallow water flow obtained from direct numerical simulation (DNS) with two different computational codes for the shallow water equations are gathered offline and subsequently employed with the aim of constructing a reduced-order correction. This is used to facilitate high-fidelity online flow predictions at much reduced costs on coarse meshes. The resolved small-scale features at high resolution represent subgrid properties for the coarse representation. Measurements of the subgrid dynamics are obtained as the difference between the evolution of a coarse grid solution and the corresponding DNS result. The measurements are sensitive to the particular numerical methods used for the simulation on coarse computational grids and can be used to approximately correct the associated discretization errors. The subgrid features are decomposed into empirical orthogonal functions (EOFs), after which a corresponding correction term is constructed. By increasing the number of EOFs in the approximation of the measured values the correction term can in principle be made arbitrarily accurate. Both computational methods investigated here show a significant decrease in the simulation error already when applying the correction based on the dominant EOFs only. The error reduction accounts for the particular discretization errors that are incurred and are hence specific to the particular simulation method that is adopted. This improvement is also observed for very coarse grids, which may be used for computational model reduction in geophysical and turbulent flow problems.
Original languageEnglish
Number of pages22
JournalMultiscale Modeling and Simulation
Issue number4
Publication statusPublished - 5 Dec 2022


  • 22/4 OA procedure
  • Empirical orthogonal functions
  • Data-driven subgrid modeling
  • Numerical simulation
  • Finite volume discretization
  • Finite element discretization
  • Shallow water equations
  • Multiscale modeling


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