On the stability of Rusanov's third-order scheme

Gottlieb, David

doi:10.1016/0021-9991(74)90121-1

Cited by 3 publications

(1 citation statement)

References 3 publications

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“…Burstein and Mirin [15] had suggested that RBM method is more appropriate for a smooth solution instead of discontinuous flow, and this remark was verified by Srinivas et al, [62] when they assessed the performance of RBM method for compressible flow. Gottlieb [63] proved that RBM is unconditionally unstable, especially in higher dimension problem. Simulation work by Darwis et al, [64] also illustrated that RBM method could not suppress shock instability.…”

Section: Average Numerical Errormentioning

confidence: 99%

Comparative Review on Computational Performance of Multistep Schemes in Solving One-Dimensional Linear Wave Equation

Hayytov

Tey

Kang

et al. 2021

CFDL

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Among several numerical methods used to solve the hyperbolic model of the linear wave equation, single-step algorithms can be the more popular ones. However, these algorithms are time-consuming while incurring numerical inaccuracy. Thus, multistep methods can be a suitable option as it has a high order of accuracy. This study aims to investigate and compare the computational performance of these multistep schemes in solving hyperbolic model based on one-dimensional linear wave equation. The techniques studied in this paper comprise the two-step Lax-Wendroff method, MacCormack method, second-order upwind method, Rusanov-Burstein-Mirin method, Warming-Kutler-Lomax method, and fourth-order Runge-Kutta method. Finite difference method is applied in discretisation. Our simulation found that although higher-order multistep methods are more stable than single-step algorithm, they suffer numerical diffusion. The two-step Lax-Wendroff method outperforms other schemes, although it is relatively simple compared with the other three and four steps schemes. The second-order upwind method is attractive as well because it is executable even with a high Courant number.

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Section: Average Numerical Errormentioning

confidence: 99%

Comparative Review on Computational Performance of Multistep Schemes in Solving One-Dimensional Linear Wave Equation

Hayytov

Tey

Kang

et al. 2021

CFDL

View full text Add to dashboard Cite

show abstract

Hyperbolic Partial Differential Equations

Lapidus¹,

Pinder²

1999

Numerical Solution of Partial Differential Equations in Science and Engineering

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The Work of David Gottlieb: A Success Story

Gustafsson

2011

Commun. comput. phys.

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Abstract. This article is a brief survey of David Gottlieb's extraordinary research career. It is impossible to give a thorough presentation of all his research and the impact of his work, but we shall describe the main contributions and give examples of the results in some of his papers. David was for many years the dominating person in the development of spectral methods, and we devote much of the space in this article to this field.

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On the stability of Rusanov's third-order scheme

Cited by 3 publications

References 3 publications

Comparative Review on Computational Performance of Multistep Schemes in Solving One-Dimensional Linear Wave Equation

Comparative Review on Computational Performance of Multistep Schemes in Solving One-Dimensional Linear Wave Equation

Hyperbolic Partial Differential Equations

The Work of David Gottlieb: A Success Story

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