Strong Stability Preserving Time Discretizations: A Review

Gottlieb, Sigal

doi:10.1007/978-3-319-19800-2_2

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Introduction and Ssp Runge-kutta Methods1

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2019

2024

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Cited by 3 publications

(1 citation statement)

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“…It has been showed that IRK methods with positive C cannot exist for p > 6 [1]. Therefore, we are interested in taking into account order conditions up to order of six.…”

Section: Introduction and Ssp Runge-kutta Methodsmentioning

confidence: 99%

Some Embedded Pairs for Optimal Implicit Strong Stability Preserving Runge–Kutta Methods

Fekete

Horváth

2019

Progress in Industrial Mathematics at ECMI 2018

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“…It has been showed that IRK methods with positive C cannot exist for p > 6 [1]. Therefore, we are interested in taking into account order conditions up to order of six.…”

Section: Introduction and Ssp Runge-kutta Methodsmentioning

confidence: 99%

Some Embedded Pairs for Optimal Implicit Strong Stability Preserving Runge–Kutta Methods

Fekete

Horváth

2019

Progress in Industrial Mathematics at ECMI 2018

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Superconvergence Analysis of the Runge–Kutta Discontinuous Galerkin Methods for a Linear Hyperbolic Equation

et al. 2020

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General non-linear fragmentation with discontinuous Galerkin methods

Lombart,

Bréhier,

Hutchison

et al. 2024

Monthly Notices of the Royal Astronomical Society

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Dust grains play a significant role in several astrophysical processes, including gas/dust dynamics, chemical reactions, and radiative transfer. Replenishment of small-grain populations is mainly governed by fragmentation during pair-wise collisions between grains. The wide spectrum of fragmentation outcomes, from complete disruption to erosion and/or mass transfer, can be modelled by the general non-linear fragmentation equation. Efficiently solving this equation is crucial for an accurate treatment of the dust fragmentation in numerical modelling. However, similar to dust coagulation, numerical errors in current fragmentation algorithms employed in astrophysics are dominated by the numerical overdiffusion problem – particularly in three-dimensional hydrodynamic simulations where the discrete resolution of the mass-density distribution tends to be highly limited. With this in mind, we have derived the first conservative form of the general non-linear fragmentation with a mass flux highlighting the mass transfer phenomenon. Then, to address cases of limited mass density resolution, we applied a high-order discontinuous Galerkin scheme to efficiently solve the conservative fragmentation equation with a reduced number of dust bins. An accuracy of $0.1{\!-\!}1~{{\ \rm per\ cent}}$ is reached with 20 dust bins spanning a mass range of 9 orders of magnitude.

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Strong Stability Preserving Time Discretizations: A Review

Cited by 3 publications

References 29 publications

Some Embedded Pairs for Optimal Implicit Strong Stability Preserving Runge–Kutta Methods

Some Embedded Pairs for Optimal Implicit Strong Stability Preserving Runge–Kutta Methods

Superconvergence Analysis of the Runge–Kutta Discontinuous Galerkin Methods for a Linear Hyperbolic Equation

General non-linear fragmentation with discontinuous Galerkin methods

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