Capturing shock waves in inelastic granular gases

Serna, Susana; Marquina, Antonio

doi:10.1016/j.jcp.2005.04.004

Cited by 20 publications

(29 citation statements)

References 22 publications

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“…Therefore, in Section 4.2, we present some preliminary investigations on applying our methods to such systems. In particular, we consider a numerical benchmark case known from the literature; a model for granular-gas flow as investigated by Serna and Marquina [33]. These initial tests seem to compare satisfactorily to results previously reported in the literature, indicating that our proposed methods may be worthy of further investigation.…”

Section: Introductionsupporting

confidence: 53%

“…We then consider the granular gas flow model studied by Serna and Marquina [33], as this example allows for comparing the performance of our method to results existing in the literature. Throughout this section, we will use the parameter…”

Section: Numerical Examplesmentioning

confidence: 99%

“…Granular gases have lately been the subject of considerable theoretical, numerical and experimental studies [9,30,29,33,31]. In this work we consider a continuum model for granular-gas flow, in which the dynamics are accounted for by a hyperbolic conservation law with relaxation.…”

Section: 2mentioning

confidence: 99%

“…In this work we consider a continuum model for granular-gas flow, in which the dynamics are accounted for by a hyperbolic conservation law with relaxation. Our main motivation for choosing this example is the existence of previously published numerical results [20,29,33], to which our simulations may be compared.…”

Section: 2mentioning

confidence: 99%

“…The dynamics of a one-dimensional granulargas flow under the influence of gravity, in the form considered by Serna and Marquina [33], can be described by the Euler-like equations…”

Section: Fluid-mechanical Equationsmentioning

confidence: 99%

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An exponential time-differencing method for monotonic relaxation systems

Aursand

Evje

Flåtten

et al. 2014

Applied Numerical Mathematics

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Abstract. We present first and second-order accurate exponential time differencing methods for a special class of stiff ODEs, denoted as monotonic relaxation ODEs. Some desirable accuracy and robustness properties of our methods are established. In particular, we prove a strong form of stability denoted as monotonic asymptotic stability, guaranteeing that no overshoots of the equilibrium value are possible. This is motivated by the desire to avoid spurious unphysical values that could crash a large simulation.We present a simple numerical example, demonstrating the potential for increased accuracy and robustness compared to established Runge-Kutta and exponential methods. Through operator splitting, an application to granulargas flow is provided.

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Section: Introductionsupporting

confidence: 53%

Section: Numerical Examplesmentioning

confidence: 99%

Section: 2mentioning

confidence: 99%

Section: 2mentioning

confidence: 99%

“…The dynamics of a one-dimensional granulargas flow under the influence of gravity, in the form considered by Serna and Marquina [33], can be described by the Euler-like equations…”

Section: Fluid-mechanical Equationsmentioning

confidence: 99%

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