High-order flux correction/finite difference schemes for strand grids

Katz, Aaron; Work, Dalon

doi:10.1016/j.jcp.2014.11.019

Cited by 42 publications

(36 citation statements)

References 42 publications

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“…Results shown in Figure 5 show third order and fourth order of acurracy for inviscid fluxes and viscous fluxes respectivel, and third order accuracy all fluxes and source terms. Furthermore, results match earlier works [4,6,15,16].…”

Section: Va Verification Studies With Manufactured Solutionssupporting

confidence: 90%

“…In order to maintain second order accuracy, only quadratic, cubic, or higher order surface elements are used. Further details of the gradient estimation may be found in our previous work [6].…”

Section: High-order Strand Grid Discretizationmentioning

confidence: 99%

“…FC is novel in that it reconstructs fluxes without the need to calculate second derivatives or higher order quadratures. The original work on FC [4,6] has been followed up with continued recent work [6,15,16] particularily in the study of higher order turbulence.…”

Section: Introductionmentioning

confidence: 99%

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High-Order Strand Grid Methods for Multi-species Reacting Flow

Blakely

Katz

Tong

2016

46th AIAA Fluid Dynamics Conference

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A higher-order method known as flux-reconstruction is employed on strand grids to model combustion. Numerical methods for discretization of governing equations on strandgrids are presented. State and transport equations for the multi-species reacting model are outlined. A description of the preconditioning techniques employed is provided. Verification via the method of manufactured solutions confirms third order accuracy. Results from idealized premixed one dimensional case show consistency between second and third order. Model is validated with experimental data from a laminar reacting boundary layer case.

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Section: Va Verification Studies With Manufactured Solutionssupporting

confidence: 90%

Section: High-order Strand Grid Discretizationmentioning

confidence: 99%

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High-Order Strand Grid Methods for Multi-species Reacting Flow

Blakely

Katz

Tong

2016

46th AIAA Fluid Dynamics Conference

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“…The high-order flux correction method, a novel method of obtaining between third-and fourth-order accuracy on strand grids, was recently investigated by Work and Katz [13] and Tong et al [30], building upon previous encouraging results designed [11,20] to address these issues. The high-order strand method involves correction of the flux in the unstructured plane, combined with stable summation-by-parts (SBP) operators [16,8] implemented as source terms to approximate flux derivatives along strands.…”

Section: Introductionmentioning

confidence: 99%

High-Order Methods for Three-Dimensional Strand-Cartesian Grids

Tong

Katz

Wissink

et al. 2015

53rd AIAA Aerospace Sciences Meeting

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The flux correction method combines unstructured flux correction along body surfaces and high-order finite differences normal to surfaces. This paper builds on previous twodimensional developments of the flux correction method and extends it to three-dimensional laminar and turbulent flow on strand grids. The development of flux correction scheme applied to three-dimensions is presented. Where turbulence modeling is required, a robust version of the Spalart-Allmaras turbulence model is employed that accommodates negative values of the turbulence working variable. A unique parallel communication strategy for high-order strand grid topologies is presented which eliminates the need for "fringe" nodes or cells in each partitioned block. A semi-implicit multigrid solution algorithm is described that allows for several advantageous solution techniques to be combined for optimal efficiency in terms of memory and computation time. Fundamental verification studies are conducted, which show the flux correction method achieves high-order accuracy for both laminar and turbulent flows. A three-dimensional steady-state study of a sphere is conducted over a range of laminar Reynolds numbers. The flux correction method accurately predicts the centers and length of recirculation vortices for each Reynolds number examined, and shows excellent comparison to experimental data. The three-dimensional unsteady capabilities of flux correction are displayed through a qualitative study of vortex shedding from a sphere.

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“…However, this approach has limitations because general unstructured grid solvers do not always work well on strand grids and it does not realize the full potential of the strand grid framework in terms of solver efficiency. In terms of development of a strand-specific flow solver, Katz and his research team [18][19][20] have developed a strand solver to address some key challenges in the strand solution methodology, but the solver is primarily a research-oriented code.…”

Section: Introductionmentioning

confidence: 99%

Application of Strand Grid Framework to Complex Rotorcraft Simulations

Lakshminarayan

Sitaraman

Wissink

2016

34th AIAA Applied Aerodynamics Conference

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The strand grid approach is a flow solution method where a prismatic-like grid using "strands" is grown to a short distance from the body surface to capture the viscous boundary layer and the rest of the domain is covered using an adaptive Cartesian grid. The approach offers several advantages in terms of nearly automatic grid generation and adaptation, ability to implement fast and efficient flow solvers that use structured data in both the strand and Cartesian grids, and the development of an efficient and highly scalable domain connectivity algorithm. An earlier work by the authors introduced a strand grid solver called mStrand, which will appear in future versions of the HPCMP CREATE TM -AV Helios framework. This paper presents application of mStrand/Helios strand grid framework for complex rotorcraft problems. The test cases presented are the UH-60A high speed forward flight and high altitude stall problems as well as the HART II blade-vortex interaction problem. The results show that the solution obtained using the strand grid framework is as good as that obtained using well-established structured and unstructured solution methodologies.

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High-order flux correction/finite difference schemes for strand grids

Cited by 42 publications

References 42 publications

High-Order Strand Grid Methods for Multi-species Reacting Flow

High-Order Strand Grid Methods for Multi-species Reacting Flow

High-Order Methods for Three-Dimensional Strand-Cartesian Grids

Application of Strand Grid Framework to Complex Rotorcraft Simulations

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