Optimized low-dispersion and low-dissipation two-derivative Runge–Kutta method for wave equations

Krivovichev, Gerasim V.

doi:10.1007/s12190-020-01339-2

Cited by 7 publications

(2 citation statements)

References 45 publications

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“…Moreover, Schlegel introduced a generic recursive multirate Runge-Kutta scheme of third order accuracy. In [18], the author developed an optimization of the explicit two-derivative sixth-order Runge-Kutta method in order to obtain low dissipation and dispersion errors. The method depends on two free parameters, used for the optimisation and the spatial derivatives are discretized by finite differences and Petrov-Galerkin approximations.…”

Section: Design Of Optimal Absolute Stability Regionsmentioning

confidence: 99%

An a posteriori strategy for adaptive schemes in time for one-dimensional advection-diffusion transport equations

Malheiro

Machado

Clain

2021

Computers & Mathematics with Applications

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Section: Design Of Optimal Absolute Stability Regionsmentioning

confidence: 99%

An a posteriori strategy for adaptive schemes in time for one-dimensional advection-diffusion transport equations

Malheiro

Machado

Clain

2021

Computers & Mathematics with Applications

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“…In Appadu et al 24 and Liska and Wendroff, 25 composite schemes which blends a dispersive scheme with a dissipative scheme to capture shock efficiently, is proposed. Low dissipation and low dispersion Runge Kutta schemes [26][27][28] have been widely used to achieve a reduction in dissipation and dispersion errors. This is mainly done by optimizing the temporal integration scheme.…”

Section: Introductionmentioning

confidence: 99%

A study of the role of weights in the spectral properties of the least square finite difference scheme and the least square upwind finite difference scheme

Mungur

2022

Numerical Methods in Fluids

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In this article, we analyze the performance of a family of nonlinear, shock-capturing mesh-free finite-difference schemes in wavenumber space. These finite difference methods are based on the use of a weighted least-square approximation procedure together with a Taylor series expansion of the unknown function. The influence of weights on the spectral properties of these schemes are studied using the approximate dispersion relation. The numerical study evidences that an appropriate choice of the weighting functions reduces dissipation and dispersion inherent to the schemes. The meshless schemes studied in this work, are then used to simulate 2D internal inviscid subsonic and transonic flows respectively in a channel with a bump. The results in 2D corroborate with the 1D analyses and reveal that when the supporting nodes closer to the reference node are assigned a greater weightage value in the computation of the 1st order spatial derivatives, better spectral properties are achieved at low wavenumber. However, the present numerical study shows that weighting function does not shift the frequency of the errors and thus in order to accelerate the convergence of these schemes, methods such as the classic multigrid can be used.

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Exponentially fitted two-derivative DIRK methods for oscillatory differential equations

Ehigie

Luân

Okunuga

et al. 2022

Applied Mathematics and Computation

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Optimized low-dispersion and low-dissipation two-derivative Runge–Kutta method for wave equations

Cited by 7 publications

References 45 publications

An a posteriori strategy for adaptive schemes in time for one-dimensional advection-diffusion transport equations

An a posteriori strategy for adaptive schemes in time for one-dimensional advection-diffusion transport equations

A study of the role of weights in the spectral properties of the least square finite difference scheme and the least square upwind finite difference scheme

Exponentially fitted two-derivative DIRK methods for oscillatory differential equations

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