Aspects of the Flux Correction Method for Solving the Navier-Stokes Equations on Unstructured Meshes

Work, Dalon; Katz, Aaron

doi:10.2514/6.2015-0834

Cited by 13 publications

(5 citation statements)

References 19 publications

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“…[20] may be employed to achieve third-order accuracy for the diffusion term. However, this particular approach requires a cubic LSQ fit and also high-order curved grids for curved geometries [31] in two and three dimensions. In this work, we focus only on methods that do not require high-order grids, and consider only the second-order scheme for diffusion in the scalar scheme.…”

Section: Iiia Discretizationmentioning

confidence: 99%

Third-Order Edge-Based Scheme for Unsteady Problems

Nishikawa

Liu

2018

2018 Fluid Dynamics Conference

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In this paper, we discuss third-order edge-based schemes for unsteady problems. Secondand third-order unconditionally-stable implicit time-integration schemes, BDF2 and ESDIRK3, are compared, and effects of different orders of time accuracy are examined. Numerical results indicate that the orders of accuracy in time and space need to match to fully take advantage of the low-dispersive feature of third-order edge-based schemes. Furthermore, the third-order scheme combined with a low-dissipation numerical flux is shown to serve as a simple and economical scheme for high-resolution simulations. The third-order low-dissipation edge-based scheme has been implemented in NASA's FUN3D with a low-dissipative Roe flux, and demonstrated for a three-dimensional unsteady viscous flow over a cylinder. Results indicate that the third-order time-accurate edge-based scheme with a low-dissipation Roe flux is a practical approach to high-fidelity unstructured-grid simulations over complex geometries.

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Section: Iiia Discretizationmentioning

confidence: 99%

Third-Order Edge-Based Scheme for Unsteady Problems

Nishikawa

Liu

2018

2018 Fluid Dynamics Conference

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“…The computational domain is schematically depicted in Figure 7. The source center is placed at r 0 = (25,20).…”

Section: Acoustic Wave Scattering By the Gaussian-core Vortexmentioning

confidence: 99%

“…At the same time, for unsteady problems it exhibits the second order of accuracy even on uniform meshes. Thanks to its robustness and rather low computational costs the FC scheme has been promptly extended to convection-diffusion problems [22] and the Navier-Stokes equations [23][24][25]. Some authors have proposed modifications of FC scheme which do provide the third order of accuracy for unsteady problems (see, in particular, [24]), however these modifications lead to significant complication of the algorithm and the loss of its conservation property.…”

Section: Introductionmentioning

confidence: 99%

Edge‐based reconstruction schemes for unstructured tetrahedral meshes

Абалакин¹,

Bakhvalov²,

Kozubskaya

2015

Numerical Methods in Fluids

101

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SUMMARYIn this paper, we consider edge-based reconstruction (EBR) schemes for solving the Euler equations on unstructured tetrahedral meshes. These schemes are based on a high-accuracy quasi-1D reconstruction of variables on an extended stencil along the edge-based direction. For an arbitrary tetrahedral mesh, the EBR schemes provide higher accuracy in comparison with most second-order schemes at rather low computational costs. The EBR schemes are built in the framework of vertex-centered formulation for the point-wise values of variables.Here, we prove the high accuracy of EBR schemes for uniform grid-like meshes, introduce an economical implementation of quasi-one-dimensional reconstruction and the resulting new scheme of EBR family, estimate the computational costs, and give new verification results.

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“…Такая схема, не требующая настроечных параметров, для решения уравнений Эйлера впервые была предложена в [2]. Хотя в рамках рёберно-ориентированного подхода, по-видимому, нельзя построить схему на-перёд заданного порядка аппроксимации, схемы этого класса -EBR [3] и метод коррекции потоков [4,5] -позволяют на практике добиваться приемлемой точ-ности при сравнительно низкой вычислительной стоимости.…”

Section: Introductionunclassified

Edge-based Approximation of the Navier – Stokes equations for axial symmetric flows on unstructured meshes

Bakhvalov

Kozubskaya

2017

KIAM Prepr.

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Aspects of the Flux Correction Method for Solving the Navier-Stokes Equations on Unstructured Meshes

Cited by 13 publications

References 19 publications

Third-Order Edge-Based Scheme for Unsteady Problems

Third-Order Edge-Based Scheme for Unsteady Problems

Edge‐based reconstruction schemes for unstructured tetrahedral meshes

Edge-based Approximation of the Navier – Stokes equations for axial symmetric flows on unstructured meshes

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