Numerical schemes for kinetic equations in the anomalous diffusion limit. Part II: degenerate collision frequency. - Inria - Institut national de recherche en sciences et technologies du numérique Access content directly
Journal Articles SIAM Journal on Scientific Computing Year : 2016

Numerical schemes for kinetic equations in the anomalous diffusion limit. Part II: degenerate collision frequency.

Abstract

In this work, which is the continuation of [9], we propose numerical schemes for linear kinetic equation which are able to deal with the fractional diffusion limit. When the collision frequency degenerates for small velocities it is known that for an appropriate time scale, the small mean free path limit leads to an anomalous diffusion equation. From a numerical point of view, this degeneracy gives rise to an additional stiffness that must be treated in a suitable way to avoid a prohibitive computational cost. Our aim is therefore to construct a class of numerical schemes which are able to undertake these stiffness. This means that the numerical schemes are able to capture the effect of small velocities in the small mean free path limit with a fixed set of numerical parameters. Various numerical tests are performed to illustrate the efficiency of our methods in this context.
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Dates and versions

hal-01245312 , version 1 (17-12-2015)

Identifiers

  • HAL Id : hal-01245312 , version 1

Cite

Nicolas Crouseilles, Hélène Hivert, Mohammed Lemou. Numerical schemes for kinetic equations in the anomalous diffusion limit. Part II: degenerate collision frequency. . SIAM Journal on Scientific Computing, 2016, 38 (4). ⟨hal-01245312⟩
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