Mesh adaptation using adjoint methods and reduced-order models for large eddy simulation

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Abstract

Adaptive mesh refinement (AMR) is potentially an effective way to automatically generate computational meshes for high-fidelity simulations such as Large Eddy Simulation (LES). Adjoint methods, which are able to localize error contributions, can be used to optimize the mesh for computing a physical quantity of interest (e.g. lift, drag) during AMR. When adjoint-based AMR techniques are applied to LES, primal flow solutions are needed to solve the adjoint problem backward in time due to the nonlinearity of Navier-Stokes equations. However, the resources required to store primal flow solutions can be huge, even prohibitive, in practical problems because of the long averaging time for computing statistical quantities. In this paper, a Reduced-Order Model (ROM) based upon Proper Orthogonal Decomposition (POD) is introduced to circumvent this issue. First, an adjoint-based error estimation procedure is verified using a manufactured solution. Then a ROM-driven AMR strategy is studied using a LES model problem based on the 1D unsteady Burgers equation. Numerical results demonstrate that using ROMs not only lowers storage requirements, but also has no impact on the effectiveness of adjoint-based AMR.

Original languageEnglish
Pages (from-to)1-11
Number of pages11
JournalWorld Congress in Computational Mechanics and ECCOMAS Congress
Volume800
DOIs
Publication statusPublished - 2021
Event14th World Congress of Computational Mechanics and ECCOMAS Congress, WCCM-ECCOMAS 2020 - Virtual, Online, Virtual, Online
Duration: 11 Jan 202115 Jan 2021

Keywords

  • Adaptive Mesh Refinement
  • Adjoint Method
  • Computational Fluid Dynamics
  • Large Eddy Simulation
  • Posterior Error Estimation
  • Reduced-Order Model

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