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Volume 24, Issue 5
An Admissible Asymptotic-Preserving Numerical Scheme for the Electronic $M_1$ Model in the Diffusive Limit

Sébastien Guisset, Stéphane Brull, Bruno Dubroca & Rodolphe Turpault

DOI: 10.4208/cicp.OA-2017-0188

Commun. Comput. Phys., 24 (2018), pp. 1326-1354.

Published online: 2018-06

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  • Abstract

This work is devoted to the derivation of an admissible asymptotic-preserving scheme for the electronic $M_1$ model in the diffusive regime. A numerical scheme is proposed in order to deal with the mixed derivatives which arise in the diffusive limit leading to an anisotropic diffusion. The derived numerical scheme preserves the realisability domain and enjoys asymptotic-preserving properties correctly handling the diffusive limit recovering the relevant limit equation. In addition, the cases of non constants electric field and collisional parameter are naturally taken into account with the present approach. Numerical test cases validate the considered scheme in the non-collisional and diffusive limits.

  • Keywords

Electronic $M_1$ moment model, approximate Riemann solvers, Godunov type schemes, asymptotic preserving schemes, diffusive limit, plasma physics, anisotropic diffusion.

  • AMS Subject Headings

65D, 65C, 76X

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{CiCP-24-1326, author = {Sébastien Guisset, Stéphane Brull, Bruno Dubroca and Rodolphe Turpault}, title = {An Admissible Asymptotic-Preserving Numerical Scheme for the Electronic $M_1$ Model in the Diffusive Limit}, journal = {Communications in Computational Physics}, year = {2018}, volume = {24}, number = {5}, pages = {1326--1354}, abstract = {

This work is devoted to the derivation of an admissible asymptotic-preserving scheme for the electronic $M_1$ model in the diffusive regime. A numerical scheme is proposed in order to deal with the mixed derivatives which arise in the diffusive limit leading to an anisotropic diffusion. The derived numerical scheme preserves the realisability domain and enjoys asymptotic-preserving properties correctly handling the diffusive limit recovering the relevant limit equation. In addition, the cases of non constants electric field and collisional parameter are naturally taken into account with the present approach. Numerical test cases validate the considered scheme in the non-collisional and diffusive limits.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.OA-2017-0188}, url = {http://global-sci.org/intro/article_detail/cicp/12480.html} }
TY - JOUR T1 - An Admissible Asymptotic-Preserving Numerical Scheme for the Electronic $M_1$ Model in the Diffusive Limit AU - Sébastien Guisset, Stéphane Brull, Bruno Dubroca & Rodolphe Turpault JO - Communications in Computational Physics VL - 5 SP - 1326 EP - 1354 PY - 2018 DA - 2018/06 SN - 24 DO - http://doi.org/10.4208/cicp.OA-2017-0188 UR - https://global-sci.org/intro/article_detail/cicp/12480.html KW - Electronic $M_1$ moment model, approximate Riemann solvers, Godunov type schemes, asymptotic preserving schemes, diffusive limit, plasma physics, anisotropic diffusion. AB -

This work is devoted to the derivation of an admissible asymptotic-preserving scheme for the electronic $M_1$ model in the diffusive regime. A numerical scheme is proposed in order to deal with the mixed derivatives which arise in the diffusive limit leading to an anisotropic diffusion. The derived numerical scheme preserves the realisability domain and enjoys asymptotic-preserving properties correctly handling the diffusive limit recovering the relevant limit equation. In addition, the cases of non constants electric field and collisional parameter are naturally taken into account with the present approach. Numerical test cases validate the considered scheme in the non-collisional and diffusive limits.

Sébastien Guisset, Stéphane Brull, Bruno Dubroca and Rodolphe Turpault. (2018). An Admissible Asymptotic-Preserving Numerical Scheme for the Electronic $M_1$ Model in the Diffusive Limit. Communications in Computational Physics. 24 (5). 1326-1354. doi:10.4208/cicp.OA-2017-0188
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