Evaluation of a High-Accuracy MacCormack-Type Scheme Using Benchmark Problems

Hixon, Ray

doi:10.1142/s0218396x9800020x

Cited by 30 publications

(28 citation statements)

References 15 publications

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“…As the time step is increased, the LDDRK 4-6 method will show an improvement over the RK4 method, as noted in Refs. [9,10]. are the nonlinear Euler equations, written in conservative form, where…”

Section: Boundary Stencil Descriptionmentioning

confidence: 99%

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Compact Implicit MacCormack-Type Schemes with High Accuracy

Hixon

Turkel

2000

Journal of Computational Physics

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Section: Boundary Stencil Descriptionmentioning

confidence: 99%

“…Recently, a new class of high-accuracy explicit MacCormack-type schemes has been introduced for computational aeroacoustics [9,10]. We extend this methodology to compact schemes, resulting in a class of highly accurate compact MacCormack-type schemes which use one-sided implicit stencils.…”

Section: Introductionmentioning

confidence: 99%

Compact Implicit MacCormack-Type Schemes with High Accuracy

Hixon

Turkel

2000

Journal of Computational Physics

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“…It is well-known [11,23] that in order to conduct satisfactory computational aeroacoustics, numerical methods must generate the least possible dispersion and dissipation errors. In general, higher order schemes would be more suitable for CAA than the lower-order schemes since, overall, the former are less dissipative [13]. This is the reason why higher-order spatial discretisation schemes have gained considerable interest in computational aeroacoustics.…”

Section: Introductionmentioning

confidence: 99%

Optimized Low Dispersion and Low Dissipation Runge-Kutta Algorithms in Computational Aeroacoustics

Appadu¹

2014

Appl. Math. Inf. Sci.

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Abstract:A new explicit fourth-order six-stage Runge-Kutta scheme with low dispersion and low dissipation properties is developed. This new Runge-Kutta scheme is shown to be more efficient in terms of dispersion and dissipation properties than existing algorithms such as Runge-Kutta temporal schemes developed by Hu et al. (1996), Mead and Renaut (1999), Tselios and Simos (2005). We perform a spectral analysis of the dispersion and dissipation errors. Numerical experiments dealing with wave propagation are performed with these four temporal Runge-Kutta schemes, all coupled with a nine-point centred difference scheme of eight order. The variation of two types of error: the error rate with respect to the L 1 norm and the Total Mean Square Error, both with respect to the CFL are obtained for all the four different schemes and it is seen that low CFL numbers are in general more effective than larger CFL numbers.

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“…It is well-known [7,14] that in order to conduct satisfactory computational aeroacoustics, numerical methods must generate the least possible dispersion and dissipation errors. In general, higher order schemes would be more suitable for CAA than the lower-order schemes since, overall, the former are less dissipative [8]. This is the reason why higher-order spatial discretisation schemes have gained considerable interest in computational aeroacoustics.…”

Section: Introductionmentioning

confidence: 99%

Applications and Spectral Analysis of some Optimized High Order Low Dispersion and Low Dissipation Schemes

Appadu¹

2014

Appl. Math. Inf. Sci.

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Abstract:In Appadu(2012d), we have used the technique of Minimized Integrated Exponential Error for Low Dispersion and Low Dissipation, (MIEELDLD) to construct high order methods with low dispersion and low dissipation properties which approximate the 1D linear advection equation. Modifications to the spatial discretisation schemes constructed by Lockard et al. (1995), Zingg et al. (1996) and Bogey and Bailly (2002) have been obtained and also a modification to the temporal scheme developed by has been devised. These novel methods obtained using MIEELDLD are more effective in terms of shock-capturing properties as they require less number of points per wavelength than the existing optimized methods for a given accuracy. In this paper, we perform some numerical experiments dealing with wave propagation with these novel as well as existing, combined spatial and temporal discretisation schemes and compare the variation of two errors namely the Total Mean Square Error and error rate with the CFL. The spectral analysis of two optimized methods made up of spatial discretisation scheme coupled with temporal discretisation scheme is also studied.

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Evaluation of a High-Accuracy MacCormack-Type Scheme Using Benchmark Problems

Abstract: Abstract

Cited by 30 publications

References 15 publications

Compact Implicit MacCormack-Type Schemes with High Accuracy

Compact Implicit MacCormack-Type Schemes with High Accuracy

Optimized Low Dispersion and Low Dissipation Runge-Kutta Algorithms in Computational Aeroacoustics

Applications and Spectral Analysis of some Optimized High Order Low Dispersion and Low Dissipation Schemes

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