Numerical treatment of the nonconservative product in a multiscale fluid model for plasmas in thermal nonequilibrium: application to solar physics. (arXiv:1806.10436v2 [math.NA] UPDATED)
<a href="http://arxiv.org/find/math/1/au:+Wargnier_Q/0/1/0/all/0/1">Quentin Wargnier</a> (CMAP), <a href="http://arxiv.org/find/math/1/au:+Faure_S/0/1/0/all/0/1">Sylvain Faure</a> (LM-Orsay), <a href="http://arxiv.org/find/math/1/au:+Graille_B/0/1/0/all/0/1">Benjamin Graille</a> (LM-Orsay), <a href="http://arxiv.org/find/math/1/au:+Magin_T/0/1/0/all/0/1">Thierry Magin</a> (VKI), <a href="http://arxiv.org/find/math/1/au:+Massot_M/0/1/0/all/0/1">Marc Massot</a> (CMAP)

This contribution deals with the modeling of collisional multicomponent
magnetized plasmas in thermal and chemical nonequilibrium aiming at simulating
and predicting magnetic reconnections in the chromosphere of the sun. We focus
on the numerical simulation of a simplified fluid model in order to properly
investigate the influence on shock solutions of a nonconservative product
present in the electron energy equation. Then, we derive jump conditions based
on travelling wave solutions and propose an original numerical treatment in
order to avoid non-physical shocks for the solution, that remains valid in the
case of coarse-resolution simulations. A key element for the numerical scheme
proposed is the presence of diffusion in the electron variables, consistent
with the physically-sound scaling used in the model developed by Graille et al.
following a multiscale Chapman-Enskog expansion method [M3AS, 19 (2009)
527–599]. The numerical strategy is eventually assessed in the framework of a
solar physics test case. The computational method is able to capture the
travelling wave solutions in both the highly- and coarsely-resolved cases.

This contribution deals with the modeling of collisional multicomponent
magnetized plasmas in thermal and chemical nonequilibrium aiming at simulating
and predicting magnetic reconnections in the chromosphere of the sun. We focus
on the numerical simulation of a simplified fluid model in order to properly
investigate the influence on shock solutions of a nonconservative product
present in the electron energy equation. Then, we derive jump conditions based
on travelling wave solutions and propose an original numerical treatment in
order to avoid non-physical shocks for the solution, that remains valid in the
case of coarse-resolution simulations. A key element for the numerical scheme
proposed is the presence of diffusion in the electron variables, consistent
with the physically-sound scaling used in the model developed by Graille et al.
following a multiscale Chapman-Enskog expansion method [M3AS, 19 (2009)
527–599]. The numerical strategy is eventually assessed in the framework of a
solar physics test case. The computational method is able to capture the
travelling wave solutions in both the highly- and coarsely-resolved cases.

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