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Numerical Modeling of Stratified Flows

We developed an Arbitrary Lagrangian-Eulerian Variational Multi-Scale (ALE-VMS) formulation aimed at the simulation of stratified flows on moving domains. The formulation couples the Navier–Stokes equations of incompressible flows with the Boussinesq approximation, and a scalar advection–diffusion equation for the density or temperature field. The proposed formulation showed good agreement with experimental results and DNS simulations reported by other researchers.

Aerodynamic simulation of atmospheric flow over the Perdigao terrain. Slice of the domain with horizontal velocity.

The framework can be used to understand the dynamic behaviour of the Atmospheric Boundary Layer (ABL) flows with different stability regimes over complex terrain, including hills and mountains; understand the effect of atmospheric stability on wind turbine wake generation and wake-turbine interaction in a context of aerodynamic and FSI analysis of multiple wind turbines; understand turbulent mixing in stratified flows and the effect of stratification on wake collapse.


  1. Y. Bazilevs, K.Takizawa, T.Tezduyar, A.Korobenko, T. Kuraishi, Y. Otoguro
    Computational aerodynamics with isogeometric analysis, Journal of Mechanics, 39, pp. 24-39, 2023

  2. H. Cen, Q. Zhou, A.Korobenko
    Isogeometric variational multiscale modeling of stably stratified flows over complex terrainsMathematical Models and Methods in Applied Sciences, 32(12), 2371-2399, 2022

  3. H. Cen, Q. Zhou, A.Korobenko
    Wall-function-based weak imposition of Dirichlet boundary condition for stratified turbulent flowsComputers & Fluids, 234, 105257, 2022

  4. H. Cen, Q. Zhou, A.Korobenko
    Simulation of stably stratified turbulent channel flow using residual-based variational multiscale method and isogeometric analysisComputers & Fluids,214, 104765, 2021

  5. A.Korobenko, J.Yan, S.M.I.Gohari, S.Sarkar, Y.Bazilevs
    FSI Simulations of Multiple Horizontal-Axis Wind Turbines Interacting with Atmospheric Boundary Layer FlowComputers & Fluids,158, 167-175, 2017

  6. J.Yan, A.Korobenko, A.Tejada-Martinez, R.Golshan, Y.Bazilevs
    A new variational multiscale formulation for stratified incompressible turbulent flows, Computers & Fluids, 158, 150-156, 2017

  7.  Y.Bazilevs, A.Korobenko, J.Yan, A.Pal, S.M.I.Gohari, S.Sarkar
    ALE-VMS Formulations for Stratified Turbulent Incompressible Flows with ApplicationsMathematical Models and Methods in Applied Science, 25(12), 2015

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