A new fourth-order non-oscillatory central scheme for hyperbolic conservation laws

Peer, Arshad Ahmud Iqbal; Gopaul, Ashvin; Dauhoo, Muhammad Zaid; Bhuruth, Muddun

doi:10.1016/j.apnum.2007.02.004

Cited by 17 publications

(27 citation statements)

References 30 publications

(40 reference statements)

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“…In this section, we report a linear stability analysis, similar to that carried out in [10,22]. In this work, we use the notation CRKS4 for the Eqs.…”

Section: Stability Analysismentioning

confidence: 99%

“…for further details see [10]. Our scheme is summarized in the following algorithm : Assuming that the cell averages {ū n j } are known, we look for the cell averages at the next time step t n+1 .…”

Section: Description Of the Fourth-order Crk Schemementioning

confidence: 99%

“…for further details see [10,24]. Also, in order to approximate the point values u n j of (8) from the cell averages {ū n j }, we put…”

Section: Description Of the Fourth-order Crk Schemementioning

confidence: 99%

“…For computing the first expression of the right hand side (6), we use the fourth-order reconstruction of Peer et al [10]. Then, we put polynomial P n j (x) on I x j := I j in the form:…”

Section: Description Of the Fourth-order Crk Schemementioning

confidence: 99%

“…The necessity of high accuracy and sharp resolution of the discontinuities motivated the development of high order techniques for conservation laws, for example, see [8][9][10]. Most high order shock capturing schemes are obtained in conservative form.…”

Section: Introductionmentioning

confidence: 99%

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A fourth‐order central Runge‐Kutta scheme for hyperbolic conservation laws

Dehghan

Jazlanian

2009

Numerical Methods Partial

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In this work, a new formulation for a central scheme recently introduced by A. A. I. Peer et al. is performed. It is based on the staggered grids. For this work, first a time discritization is carried out, followed by the space discritization. Spatial accuracy is obtained using a piecewise cubic polynomial and fourth-order numerical derivatives. Time accuracy is obtained applying a Runge-Kutta(RK) scheme. The scheme proposed in this work has a simpler structure than the central scheme developed in (Peer et al., Appl Numer Math 58 (2008), 674-688). Several standard one-dimensional test cases are used to verify high-order accuracy, nonoscillatory behavior, and good resolution properties for smooth and discontinuous solutions.

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“…In this section, we report a linear stability analysis, similar to that carried out in [10,22]. In this work, we use the notation CRKS4 for the Eqs.…”

Section: Stability Analysismentioning

confidence: 99%

Section: Description Of the Fourth-order Crk Schemementioning

confidence: 99%

“…for further details see [10,24]. Also, in order to approximate the point values u n j of (8) from the cell averages {ū n j }, we put…”

Section: Description Of the Fourth-order Crk Schemementioning

confidence: 99%

“…For computing the first expression of the right hand side (6), we use the fourth-order reconstruction of Peer et al [10]. Then, we put polynomial P n j (x) on I x j := I j in the form:…”

Section: Description Of the Fourth-order Crk Schemementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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A fourth‐order central Runge‐Kutta scheme for hyperbolic conservation laws

Dehghan

Jazlanian

2009

Numerical Methods Partial

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Sodium Ion Dynamics in the Magnetospheric Flanks of Mercury

Aizawa

Delcourt

Terada

2018

Geophysical Research Letters

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We investigate the transport of planetary ions in the magnetospheric flanks of Mercury. In situ measurements from the MErcury Surface, Space ENvironment, GEochemistry, and Ranging spacecraft show evidences of Kelvin‐Helmholtz instability development in this region of space, due to the velocity shear between the downtail streaming flow of solar wind originating protons in the magnetosheath and the magnetospheric populations. Ions that originate from the planet exosphere and that gain access to this region of space may be transported across the magnetopause along meandering orbits. We examine this transport using single‐particle trajectory calculations in model Magnetohydrodynamics simulations of the Kelvin‐Helmholtz instability. We show that heavy ions of planetary origin such as Na+ may experience prominent nonadiabatic energization as they E × B drift across large‐scale rolled up vortices. This energization is controlled by the characteristics of the electric field burst encountered along the particle path, the net energy change realized corresponding to the maximum E × B drift energy. This nonadiabatic energization also is responsible for prominent scattering of the particles toward the direction perpendicular to the magnetic field.

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A new reconstruction procedure in central schemes for hyperbolic conservation laws

Balaguer-Beser

2011

Numerical Meth Engineering

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SUMMARYThis paper presents a new point value reconstruction algorithm based on average values or flux values for central Runge-Kutta schemes in the resolution of hyperbolic conservation laws. This reconstruction employs a fourth-order accurate approximation of point values of the solution at the two extrema and at the mid-point of each cell. These point values are modified in order to enforce monotonicity and shape preserving properties. This correction has been applied essentially in the cells close to the maxima and minima of the solution and in these cases, it has been proven that the reconstruction is fourth-order accurate. In the cells with a maximum or minimum of the solution, a correction has also been applied to such point values with the aim of ensuring that the resulting numerical solution has a non-oscillatory behavior. Several standard one-and two-dimensional test cases are used to verify high-order accuracy, non-oscillatory behavior and high-resolution properties for smooth and discontinuous solutions, and also in their componentwise extension to the Euler gas dynamics equations.

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A new fourth-order non-oscillatory central scheme for hyperbolic conservation laws

Cited by 17 publications

References 30 publications

A fourth‐order central Runge‐Kutta scheme for hyperbolic conservation laws

A fourth‐order central Runge‐Kutta scheme for hyperbolic conservation laws

Sodium Ion Dynamics in the Magnetospheric Flanks of Mercury

A new reconstruction procedure in central schemes for hyperbolic conservation laws

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