Analysis of super compact finite difference method and application to simulation of vortex–shock interaction

Fu, Dexun; Ma, Yanwen

doi:10.1002/fld.155

Cited by 10 publications

(5 citation statements)

References 12 publications

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“…It has been extensively studied experimentally (e.g. Dosanjh and Weeks [1965], Cattafesta and Settles [1992], Chang et al [2004]), analytically (Ribner [1954a(Ribner [ , 1985, Mahesh et al [1997]) and numerically (Ellzey et al [1995], Inoue and Hattori [1999], Dexun and Yanwen [2001]), with a particular emphasis on the noise production through the interaction. The passage of large coherent vortices through compression wave contributes significantly to the shock-associated noise that is found in jet engines.…”

Section: Shock / Vortex Interactionmentioning

confidence: 99%

Hybrid LES of Detonations in Reacting Multi-Phase Mixtures

Menon¹,

Génin²

2009

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REPORT DOCUMENTATION PAGEThe public reporting burden for this collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources gathering and maintaining the data needed, and completing and reviewing the collection of information. Send comments regarding this burden estimate or any other aspect of this collection of information, including suggestions for reducing the burden, to Department of Defense, Washington Headquarters Services, Directorate for Information Operations and Reports (0704-0188), 1215 Jefferson Davis Highway, Suite 1204, Arlington, VA 22202-4302. Respondents should be aware that notwithstanding any other provision of law, no person shall be subject to any penalty for failing to comply with a collection of information if it does not display a currently valid 0MB control number. PLEASE DO NOT RETURN YOUR FORM TO THE ABOVE ADDRESS. REPORT DATE (DD-MM-YYYY) 28-02-2009 2. REPORT TYPE Final Report DATES COVERED {From -To)December 1 PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES)School of Aerospace Engineering Georgia Institute of Technology Atlanta, GA 30332 PERFORMING ORGANIZATION REPORT NUMBERCCL-TR-2009-02-1 SPONSORING/MONITORING AGENCY NAME(S) AND ADDRESS(ES)AFOSR/NL 4015 Wilson Blvd ? Arlington, VA 22203 Dr. Fariba Fahroo SPONSOR/MONITORS ACRONYM(S)AFOSR/NM SPONSOR/MONITORS REPORT NUMBER(S) DISTRIBUTION/AVAILABILITY STATEMENTUnlimited, Unclassified SUPPLEMENTARY NOTES ABSTRACTA Large-Eddy Simulation (LES) methodology adapted to the resolution of high Reynolds number turbulent flows in supersonic conditions was proposed and developed. A novel numerical scheme was designed, that switches from a low-dissipation central scheme for turbulence resolution to a flux difference splitting scheme in regions of discontinuities. A state-of-the-art closure model was extended in order to take compressibility effects and the action of shock / turbulence interaction into account. The proposed method was validated and employed for the study of shock / turbulent shear layer interaction as a mixing-augmentation technique, and highlighted the efficiency in mixing improvement after the interaction, but also the limited spatial extent of this turbulent enhancement. A second study focused on the injection of a sonic jet normally to a supersonic crossflow. The validity of the simulation was assessed by comparison with experimental data, and the dynamics of the interaction was examined. The sources of vortical structures were identified, with a particular emphasis on the impact of the flow speed onto the vortical evolution. It is shown that the developed hybrid methodology permits a capture of shock / turbulence interactions in direct simulations that agrees well with other reference simulations, and that the LES methodology effectively reproduces the turbulence evolution and physical phenomena involved in the interaction. This numerical approach is then employed to study a problem of practical importance in high-speed mixing. The inter...

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Section: Shock / Vortex Interactionmentioning

confidence: 99%

Hybrid LES of Detonations in Reacting Multi-Phase Mixtures

Menon¹,

Génin²

2009

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“…A recent development in compact schemes has been the introduction of a general procedure to generate highly accurate schemes of arbitrary order with minimal stencil size by Dexun and Yanwen (1995), who called it the 'Super Compact Finite-Difference Method' (SCFDM). The derivation and the application of the method in a uniform grid have been presented by Yanwen and Dexun (1996) and by Dexun and Yanwen (2001).…”

Section: Introductionmentioning

confidence: 99%

“…The derivation and the application of the method in a uniform grid have been presented by Yanwen and Dexun (1996) and by Dexun and Yanwen (2001). In addition, some aspects of the scheme in a non-uniform grid have been investigated by Ghader (2000) and Esfahanian et al (2004).…”

Section: Introductionmentioning

confidence: 99%

“…Motivated by the strong performance of the sixth-order SCFDM compared with a traditional explicit and a compact scheme of the same order in simulating vortex-shock interaction for compressible Navier-Stokes equations (Dexun and Yanwen 2001), this paper is devoted to the assessment of the accuracy of SCFDM in the atmosphere-ocean dynamics context. To this end, we apply the second-, fourth-, and sixth-order SCFDM to spatial differencing of some prototype linear and nonlinear geophysical fluid dynamics problems.…”

Section: Introductionmentioning

confidence: 99%

“…Compared with the traditional explicit finite-difference schemes of the same order, compact schemes have proved to be significantly more accurate with the added benefit of using smaller stencil sizes, which can be essential when treating non-periodic boundary conditions. A recent development in compact schemes has been the introduction of a general procedure to generate highly accurate schemes of arbitrary order with minimal stencil size by Dexun and Yanwen (1995), who called it the 'Super Compact Finite-Difference Method' (SCFDM). The derivation and the application of the method in a uniform grid have been presented by Yanwen and Dexun (1996) and by Dexun and Yanwen (2001).…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

On the use of the super compact scheme for spatial differencing in numerical models of the atmosphere

Esfahanian

Ghader

Mohebalhojeh

2005

Quart J Royal Meteoro Soc

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SUMMARYThe 'Super Compact Finite-Difference Method' (SCFDM) is applied to spatial differencing of some prototype linear and nonlinear geophysical fluid dynamics problems. An alternative form of the SCFDM relations for spatial derivatives is derived. The sixth-order SCFDM is compared in detail with the conventional fourthorder compact and the second-order centred differencing. For the frequency of linear inertia-gravity waves on different numerical grids (Arakawa's A-E and Randall's Z) related to the Rossby adjustment process, the sixthorder SCFDM shows a substantial improvement on the conventional methods. For the Jacobians involved in vorticity advection by non-divergent flow and in the Bolin-Charney balance equation, a general framework, valid for every finite-difference method, is derived to present the discrete forms of the Jacobians. It is found that the sixth-order SCFDM provides a noticeably more accurate representation of the wave-number distribution of the Jacobians, when compared with the conventional methods. The problem of reconstructing the stream-function field from the vorticity field on a sphere is also considered. For the Rossby-Haurwitz wave, the computation of a normalized global error at different horizontal resolutions in longitude and latitude directions shows that the sixthorder SCFDM can markedly improve on the fourth-order compact. The sixth-order SCFDM is thus proposed as a viable method to improve the accuracy of finite-difference models of the atmosphere.

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Accuracy analysis of super compact scheme in non‐uniform grid with application to parabolized stability equations

Esfahanian

Ghader

Ashrafi

2004

Numerical Methods in Fluids

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SUMMARYA brief derivation of the super compact ÿnite di erence method (SCFDM) in non-uniform grid points is presented. To investigate the accuracy of the SCFDM in non-uniform grid points the Fourier analysis is performed. The Fourier analysis shows that the grid aspect ratio plays a crucial role in the accuracy of the SCFDM in a non-uniform grid. It is also found that the accuracy of the higher order relations of the SCFDM is more sensitive to grid aspect ratio than the lower order relations. In addition, to obtain a mathematical representation of the accuracy and making clear the role of the aspect ratio in the accuracy of the SCFDM in non-uniform grids, the modiÿed equation approach is used. For the sake of demonstrating the analytical results obtained from the Fourier analysis and the modiÿed equation approach, the super compact ÿnite di erence method is applied to solve the Blasius boundary layer and the non-linear parabolized stability equations as numerical examples indicating the di culty with non-uniform grid spacing using the super compact scheme.

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Analysis of super compact finite difference method and application to simulation of vortex–shock interaction

Cited by 10 publications

References 12 publications

Hybrid LES of Detonations in Reacting Multi-Phase Mixtures

Hybrid LES of Detonations in Reacting Multi-Phase Mixtures

On the use of the super compact scheme for spatial differencing in numerical models of the atmosphere

Accuracy analysis of super compact scheme in non‐uniform grid with application to parabolized stability equations

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