On Applications of High Resolution Shock Capturing Methods to Unsteady Flows

Causon, D. M.; Ingram, David; Yang, Guowei

doi:10.1007/978-94-015-9137-9_6

Cited by 3 publications

(3 citation statements)

References 12 publications

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“…The use of Fourier representation, given by Equation (5), in this computational molecule gives the numerical dispersion relation Figure 4. The DRP region in non-dimensional wave number-frequency for the slope limiter scheme [6] for the same values of h shown in Figure 3.…”

Section: Resultsmentioning

confidence: 95%

“…This method is adopted in Causon et al [6], for developing high-resolution shock capturing scheme for transient analysis. The piecewise interpolation for reconstruction requires maintaining the positivity by eliminating non-physical oscillation.…”

Section: Slope Limiter Schemementioning

confidence: 99%

“…In this research the same is extended to investigate stability and the dispersion property of some of the traditional methods as well as a new scheme that uses a slope limiter [6] to control non-linear numerical instability for spatial discretization. Additionally, various time-integration schemes that are used for DNS and LES, namely the Adams-Bashforth and multistage Runge -Kutta schemes are also investigated.…”

Section: Introductionmentioning

confidence: 98%

See 2 more Smart Citations

Spectral analysis of flux vector splitting finite volume methods

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Sridar

Sarkar

et al. 2001

Numerical Methods in Fluids

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SUMMARYNew results are presented here for finite volume (FV) methods that use flux vector splitting (FVS) along with higher-order reconstruction schemes. Apart from spectral accuracy of the resultant methods, the numerical stability is investigated which restricts the allowable time step or the Courant -Friedrich -Lewy (CFL) number. Also the dispersion relation preservation (DRP) property of various spatial and temporal discretization schemes is investigated. The DRP property simultaneously fixes space and time steps. This aspect of numerical schemes is important for simulation of high-Reynolds number flows, compressible flows with shock(s) and computational aero-acoustics. It is shown here that for direct numerical simulation applications, the DRP property is more restrictive than stability criteria.