Length-scales for efficient CFL conditions in high-order methods with distorted meshes: Application to local-timestepping for p-multigrid

Saumitra Joshi, Jiaqing Kou, Aurelio Hurtado de Mendoza, Kunal Puri, Charles Hirsch, Gonzalo Rubio, Esteban Ferrer

Research output: Contribution to journalArticlepeer-review

5 Scopus citations

Abstract

We propose a strategy to estimate the maximum stable time-steps for explicit time-stepping methods for hyperbolic systems in a high-order flux reconstruction framework. The strategy is derived through a von-Neumann analysis (VNA) framework for the advection–diffusion equation on skewed two- and three-dimensional meshes. It directly incorporates the spatial polynomial- and mesh-discretization in estimating the convective and diffusive length-scales. The strategy is extended to the density-based Navier–Stokes system of equations, taking into account the omnidirectionality of the speed of sound. We compare the performance of this strategy with three other popular choices of length-scales across a wide range of polynomial-orders, meshes of drastically varying cell-quality, and flow-physics. The proposed strategy shows robust behavior across all test-scenarios with limited variation of the maximum stable CFL-number (0.1 to 1) for polynomial-orders 1 through 10, unlike other strategies where the CFL-number varies sharply. Finally, we show the advantage of the proposed methodology for local-timestepping for p-multigrid through a RANS-modeled steady-state turbulent flow case, on a mesh with large disparity of mesh elements and aspect ratios.

Original languageEnglish
Article number106011
JournalComputers and Fluids
Volume265
DOIs
StatePublished - 30 Oct 2023
Externally publishedYes

Keywords

  • CFL
  • Distorted
  • High-order
  • Length-scale
  • Skewed
  • Timestep

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