A comparison of higher-order finite-difference shock capturing schemes

Brehm, Christoph; Barad, Michael F.; Housman, Jeffrey A.; Kiris, Cetin C.

doi:10.1016/j.compfluid.2015.08.023

Cited by 95 publications

(32 citation statements)

References 37 publications

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“…Here, the LAD approach to capture shock waves and contacts with density differences is extended to multiphase flows using the AD fluxes obtained in the previous section. The proposed AD terms maintain equilibrium across the multiphase fluid interfaces with varying densities.…”

Section: Numerical Implementationmentioning

confidence: 99%

“…These schemes have been designed to work with high-order central schemes (usually greater than the fourth) in an attempt to capture the smallest scales. 27,29,32 Here, the LAD approach to capture shock waves 33 and contacts with density differences is extended to multiphase flows using the AD fluxes obtained in the previous section. The proposed AD terms maintain equilibrium across the multiphase fluid interfaces with varying densities.…”

Section: Localized Artificial Diffusivity: Lad Schemementioning

confidence: 99%

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A localized artificial diffusivity method to simulate compressible multiphase flows using the stiffened gas equation of state

Aslani

Regele

2018

Numerical Methods in Fluids

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Summary The development of numerical approaches to perform direct numerical simulations of compressible multiphase flows has been an active field of research for several years. Proper treatment of fluid interfaces is crucial as important physics occur in this infinitesimally small region. Furthermore, the compressibility of the fluid requires proper treatment of discontinuities. Artificial diffusivity is among a number of methods widely used for compressible flows. This study develops a general form of consistent artificial diffusion fluxes and extends the localized artificial diffusivity method for high‐order central schemes to solve multiphase flows with an interface‐capturing method. These fluxes ensure an oscillation‐free interface for pressure, velocity, and temperature without employing a sharpening technique. Moreover, the high‐order representation of all scales in the flow helps capture the wide range of instabilities inherent in these flows. The goal is to develop an approach capable of performing high‐fidelity simulations supported by physics‐driven validation. This is achieved by solving the five‐equation model with the stiffened‐gas equation of state using the proposed method for multicomponent and multiphase flows on a variety of 1D and 2D problems.

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Section: Numerical Implementationmentioning

confidence: 99%

Section: Localized Artificial Diffusivity: Lad Schemementioning

confidence: 99%

A localized artificial diffusivity method to simulate compressible multiphase flows using the stiffened gas equation of state

Aslani

Regele

2018

Numerical Methods in Fluids

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“…[14][15][16][17] A thorough study comparing several high-order finitedifference methods on Cartesian grids within the LAVA framework was reported previously. 18 Results from this study indicated that high-order Weighted Essentially Non-Oscillatory (WENO) schemes 19 performed well in both resolution (Points-Per-Wavelength PPW), shock capturing, and robustness under harsh flow conditions. A natural extension of finite-difference WENO schemes to curvilinear grids are the high-order Weighted Compact Nonlinear Schemes (WCNS).…”

Section: Iiia1 Low Dissipation Finite-difference Methodsmentioning

confidence: 92%

Application of Lattice Boltzmann and Navier-Stokes Methods to NASA’s Wall Mounted Hump

Kiris

Stich

Housman

et al. 2018

2018 Fluid Dynamics Conference

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Lattice Boltzmann (LB) based Large Eddy Simulation (LES), Reynolds-averaged Navier-Stokes (RANS) as well as hybrid RANS/LES methods within the Launch Ascent and Vehicle Aerodynamics (LAVA) solver framework are applied to NASA's wall-mounted hump. Computational results are compared with experiments performed by Greenblatt et al. 1 A detailed comparison between the accuracy and resolution requirements of the two approaches for turbulence resolving simulations, as well as the suitability of different grid paradigms (body-fitted curvilinear and block structured Cartesian) are presented. This test case is part of NASA's Revolutionary Computational Aerosciences (RCA) sub-project which addresses the technical challenge of predicting flow separation and reattachment accurately. Improvements in predictive accuracy by as much as 90% are demonstrated using LB as well as hybrid RANS/LES approaches compared to state-of-the-art steady state

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“…There are a lot available finite difference schemes in the literature such as artificial dissipation (AD), localized artificial diffusivity (LAD) and weighted essentially non-oscillatory (WENO) schemes. Those are high order schemes as previously described by [9]. The shallow water equations can be solved using the ordinary finite difference methods such as Lax-Friederichs and Lax-Wendroff numerical schemes.…”

Section: Methodsmentioning

confidence: 99%

Deficiency of finite difference methods for capturing shock waves and wave propagation over uneven bottom seabed

Ahmad¹,

Suliman²,

2018

IJET

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The implementation of finite difference method is used to solve shallow water equations under the extreme conditions. The cases such as dam break and wave propagation over uneven bottom seabed are selected to test the ordinary schemes of Lax-Friederichs and Lax-Wendroff numerical schemes. The test cases include the source term for wave propagation and exclude the source term for dam break. The main aim of this paper is to revisit the application of Lax-Friederichs and Lax-Wendroff numerical schemes at simulating dam break and wave propagation over uneven bottom seabed. For the case of the dam break, the two steps of Lax-Friederichs scheme produce nonoscillation numerical results, however, suffering from some of dissipation. Moreover, the two steps of Lax-Wendroff scheme suffers a very bad oscillation. It seems that these numerical schemes cannot solve the problem at discontinuities which leads to oscillation and dissipation. For wave propagation case, those numerical schemes produce inaccurate information of free surface and velocity due to the uneven seabed profile. Therefore, finite difference is unable to model shallow water equations under uneven bottom seabed with high accuracy compared to the analytical solution.

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A comparison of higher-order finite-difference shock capturing schemes

Cited by 95 publications

References 37 publications

A localized artificial diffusivity method to simulate compressible multiphase flows using the stiffened gas equation of state

A localized artificial diffusivity method to simulate compressible multiphase flows using the stiffened gas equation of state

Application of Lattice Boltzmann and Navier-Stokes Methods to NASA’s Wall Mounted Hump

Deficiency of finite difference methods for capturing shock waves and wave propagation over uneven bottom seabed

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