High-resolution numerical simulation of turbulence in natural waterways

Seokkoo Kang, Anne Lightbody, Craig Hill, Fotis Sotiropoulos

Research output: Contribution to journalArticlepeer-review

139 Scopus citations


We develop an efficient and versatile numerical model for carrying out high-resolution simulations of turbulent flows in natural meandering streams with arbitrarily complex bathymetry. The numerical model solves the 3D, unsteady, incompressible Navier-Stokes and continuity equations in generalized curvilinear coordinates. The method can handle the arbitrary geometrical complexity of natural streams using the sharp-interface curvilinear immersed boundary (CURVIB) method of Ge and Sotiropoulos (2007) [1]. The governing equations are discretized with three-point, central, second-order accurate finite-difference formulas and integrated in time using an efficient, second-order accurate fractional step method. To enable efficient simulations on grids with tens of millions of grid nodes in long and shallow domains typical of natural streams, the algebraic multigrid (AMG) method is used to solve the Poisson equation for the pressure coupled with a matrix-free Krylov solver for the momentum equations. Depending on the desired level of resolution and available computational resources, the numerical model can either simulate, via direct numerical simulation (DNS), large-eddy simulation (LES), or unsteady Reynolds-averaged Navier-Stokes (URANS) modeling. The potential of the model as a powerful tool for simulating energetic coherent structures in turbulent flows in natural river reaches is demonstrated by applying it to carry out LES and URANS in a 50-m long natural meandering stream at resolution sufficiently fine to capture vortex shedding from centimeter-scale roughness elements on the bed. The accuracy of the simulations is demonstrated by comparisons with experimental data and the relative performance of the LES and URANS models is also discussed.

Original languageEnglish (US)
Pages (from-to)98-113
Number of pages16
JournalAdvances in Water Resources
Issue number1
StatePublished - Jan 2011

Bibliographical note

Funding Information:
This work was supported by NSF Grants EAR-0120914 (as part of the National Center for Earth-Surface Dynamics) and EAR-0738726 and a Grant from Yonsei University, South Korea . Computational resources were provided by the University of Minnesota Supercomputing Institute.


  • Immersed boundary method
  • Large-eddy simulation
  • Navier-Stokes equation
  • Reynolds-averaged Navier-Stokes modeling
  • Stream flow


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