Filtering techniques for complex geometry fluid flows

Mullen, Julie S.; Fischer, Paul

doi:10.1002/(sici)1099-0887(199901)15:1<9::aid-cnm219>3.0.co;2-y

Cited by 57 publications

(55 citation statements)

References 9 publications

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“…The filters are all applied locally within each element, which is a key factor in keeping the cost down: global filtering operations for spectral element methods [31] are expensive as they necessitate solving global equations, and are possibly not particularly relevant for application of the DP, where the concentration is on the smallest length scales. In essence, the filters are all spectral filters, but the shape functions to which they are applied have only local support, so the filters can be sharp in spectral space but local in physical space.…”

Section: Introductionmentioning

confidence: 85%

Spectral element filtering techniques for large eddy simulation with dynamic estimation

Blackburn

Schmidt

2003

Journal of Computational Physics

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Spectral element methods have previously been successfully applied to direct numerical simulation of turbulent flows with moderate geometrical complexity and low to moderate Reynolds numbers. A natural extension of application is to large eddy simulation of turbulent flows, although there has been little published work in this area. One of the obstacles to such application is the ability to deal successfully with turbulence modelling in the presence of solid walls in arbitrary locations. An appropriate tool with which to tackle the problem is dynamic estimation of turbulence model parameters, but while this has been successfully applied to simulation of turbulent wall-bounded flows, typically in the context of spectral and finite volume methods, there have been no published applications with spectral element methods. Here, we describe approaches based on element-level spectral filtering, couple these with the dynamic procedure, and apply the techniques to large eddy simulation of a prototype wall-bounded turbulent flow, the plane channel, using a mixing length-based eddy viscosity subgrid-scale model. The methods outlined here may be carried over without modification to more complex geometries.

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Section: Introductionmentioning

confidence: 85%

Spectral element filtering techniques for large eddy simulation with dynamic estimation

Blackburn

Schmidt

2003

Journal of Computational Physics

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“…Thus, (8) is closely related to the idea of low-pass differential filters, see, e.g., [20]. The results for the discrete decomposition (8) with α = 4 are shown in the right part of Table 2.…”

Section: Staggered Grid Discretization and The Helmholtz Decompositionmentioning

confidence: 99%

“…If the Navier-Stokes solution is sufficiently smooth and one computes drag and lift coefficients of a finite element numerical solution, then it is proved in [37] that using the volume based formulas (21) gives more accurate values of drag and lift coefficients compared to (19) and (20). Although for this test problem the solution is not regular, it turned out that using (21) still leads to more accurate results.…”

Section: Oyzmentioning

confidence: 99%

An octree-based solver for the incompressible Navier–Stokes equations with enhanced stability and low dissipation

Olshanskii¹,

Terekhov²,

Vassilevski³

2013

Computers & Fluids

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The paper introduces a finite difference solver for the unsteady incompressible Navier-Stokes equations based on adaptive cartesian octree grids. The method extends a stable staggered grid finite difference scheme to the graded octree meshes. It is found that a straightforward extension is prone to produce spurious oscillatory velocity modes on the fine-to-coarse grids interfaces. A local linear low-pass filter is shown to reduce much of the bad influence of the interface modes on the accuracy of numerical solution. We introduce an implicit upwind finite difference approximation of advective terms as a low dissipative and stable alternative to semi-Lagrangian methods to treat the transport part of the equations. The performance of method is verified for a set of benchmark tests: a Beltrami type flow, the 3D lid-driven cavity and channel flows over a 3D square cylinder.

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“…(See [5,21] and references therein.) Spectral based filtering methods often have difficultities in handling problems on irregular domains.…”

Section: F (U ∇U) = − K(s(u)) µ ∇U Exhibits Different Behaviors Basementioning

confidence: 99%

Stabilized approximation to degenerate transport equations via filtering

Ervin

Jenkins

2011

Applied Mathematics and Computation

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We analyze a stabilization technique for advection dominated flow problems. Of particular interest are coupled parabolic/hyperbolic problems, when the diffusion coefficient is zero in part of the domain. The unstabilized, computed approximations of these problems are highly oscillatory, and several techniques have been proposed and analyzed to mitigate the effects of the subgrid errors that contribute to the oscillatory behavior. In this paper, we modify a timerelaxation algorithm proposed in [1] and further studied in [10]. Our modification introduces the relaxation operator as a post-processing step. The operator is not time-dependent, so the discrete (relaxation) system need only be factored once. We provide convergence analysis for our algorithm along with numerical results for several model problems.

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Filtering techniques for complex geometry fluid flows

Cited by 57 publications

References 9 publications

Spectral element filtering techniques for large eddy simulation with dynamic estimation

Spectral element filtering techniques for large eddy simulation with dynamic estimation

An octree-based solver for the incompressible Navier–Stokes equations with enhanced stability and low dissipation

Stabilized approximation to degenerate transport equations via filtering

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