Multi-dimensional finite volume scheme for the vorticity transport equations

Foti, Daniel; Duraisamy, Karthik

doi:10.1016/j.compfluid.2018.02.024

Cited by 12 publications

(7 citation statements)

References 37 publications

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“…In order to account for the fluxes traveling oblique to the cell faces while simultaneously increasing numerical stability and accuracy, transverse fluxes are included. The transverse directional flux functions G are computed using the flux-based wave propagation approach [45]. All flux functions are stored at the cell faces.…”

Section: Multi-dimensional Upwind Finite Volumementioning

confidence: 99%

“…In many vortex-dominated problems, especially those in which the vorticity distribution is compact [41][42][43] the vorticity-velocity formulation of the Navier-Stokes equations has the potential to be advantageous in comparison to the pressure-velocity form [44,45]. Despite the use of a wide array of Eulerian [46,47], Lagrangian [48,49] and mixed numerical implementations [50,51] of the vorticity transport equations, modeling of unresolved dynamics remains an outstanding issue.…”

Section: Introductionmentioning

confidence: 99%

“…On the other hand, relatively few Eulerian vorticity numerical schemes have been developed [46,56,57]. Recently developed upwind finite volume methods for the VTE [45,47,58] have been shown to efficiently capture and preserve vortical structures with relatively coarse resolution (a few grid cells spanning vortex cores). Consistent integration of both the vorticity convection and vortex stretching terms is a prominent feature of schemes in Refs.…”

Section: Introductionmentioning

confidence: 99%

“…Consistent integration of both the vorticity convection and vortex stretching terms is a prominent feature of schemes in Refs. [45,58]. While these schemes fit into the philosophy of ILES, an understanding of their sub-grid scale behavior has not been established in the context of turbulent flows.…”

Section: Introductionmentioning

confidence: 99%

“…A minimum state of scale separation is necessary to reproduce high Reynolds numbers flows with asymptotic turbulence statistics [36,59]. In this work, we will examine the utility of a finite volume scheme for the VTE [45,58], characterizes its ILES properties and provide a methodology to estimate effective Reynolds numbers. This particular formulation has a number of features pertinent for ILES: Consistent integration of vorticity convection and vortex stretching terms, promoting stability and accuracy and the ability to represent and preserve sharp gradients.…”

Section: Introductionmentioning

confidence: 99%

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Sub-grid scale characterization and asymptotic behavior of multi-dimensional upwind schemes for the vorticity transport equations

Foti¹,

Duraisamy²

2021

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We study the sub-grid scale characteristics of a vorticity-transport-based approach for large-eddy simulations. In particular, we consider a multi-dimensional upwind scheme for the vorticity transport equations and establish its properties in the underresolved regime. The asymptotic behavior of key turbulence statistics of velocity gradients, vorticity, and invariants is studied in detail. Modified equation analysis indicates that dissipation can be controlled locally via non-linear limiting of the gradient employed for the vorticity reconstruction on the cell face such that low numerical diffusion is obtained in well-resolved regimes and high numerical diffusion is realized in under-resolved regions. The enstrophy budget highlights the remarkable ability of the truncation terms to mimic the true sub-grid scale dissipation and diffusion. The modified equation also reveals diffusive terms that are similar to several commonly employed sub-grid scale models including tensor-gradient and hyper-viscosity models. Investigations on several canonical turbulence flow cases show that large-scale features are adequately represented and remain consistent in terms of spectral energy over a range of grid resolutions. Numerical dissipation in under-resolved simulations is consistent and can be characterized by diffusion terms discovered in the modified equation analysis. A minimum state of scale separation necessary to obtain asymptotic behavior is characterized using metrics such as effective Reynolds number and effective grid spacing. Temporally-evolving jet simulations, characterized by large-scale vortical structures, demonstrate that high Reynolds number vortex-dominated flows are captured when criteria is met and necessitate diffusive non-linear limiting of vorticity reconstruction be employed to realize accuracy in under-resolved simulations.

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Section: Multi-dimensional Upwind Finite Volumementioning

confidence: 99%