IMEX and exact sequence discretization of the multi-fluid plasma model
Abstract
Multi-fluid plasma models, where an electron fluid is modeled in addition to multiple ion and neutral species as well as the full set of Maxwell's equations, are useful for representing physics beyond the scope of classic MHD. This advantage presents challenges in appropriately dealing with electron dynamics and electromagnetic behavior characterized by the plasma and cyclotron frequencies and the speed of light. For physical systems, such as those near the MHD asymptotic regime, this requirement drastically increases runtimes for explicit time integration even though resolving fast dynamics may not be critical for accuracy. Implicit time integration methods, with efficient solvers, can help to step over fast time-scales that constrain stability, but do not strongly influence accuracy. As an extension, Implicit-explicit (IMEX) schemes provide an additional mechanism to choose which dynamics are evolved using an expensive implicit solve or resolved using a fast explicit solve. In this study, in addition to IMEX methods we also consider a physics compatible exact sequence spatial discretization. Here, this combines nodal bases (H-Grad) for fluid dynamics with a set of vector bases (H-Curl and H-Div) for Maxwell's equations. This discretization allows for multi-fluid plasma modeling without violating Gauss' laws for the electric and magnetic fields.more »
- Authors:
-
- Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
- Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Univ. of New Mexico, Albuquerque, NM (United States)
- Publication Date:
- Research Org.:
- Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
- Sponsoring Org.:
- USDOE National Nuclear Security Administration (NNSA)
- OSTI Identifier:
- 1559495
- Alternate Identifier(s):
- OSTI ID: 1691625
- Report Number(s):
- SAND-2019-8520J
Journal ID: ISSN 0021-9991; 677744; TRN: US2000350
- Grant/Contract Number:
- AC04-94AL85000; NA0003525
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Journal of Computational Physics
- Additional Journal Information:
- Journal Volume: 397; Journal ID: ISSN 0021-9991
- Publisher:
- Elsevier
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 70 PLASMA PHYSICS AND FUSION TECHNOLOGY; Multi-fluid plasmas; Exact sequence discretizations; IMEX; Finite element methods
Citation Formats
Miller, Sean T., Cyr, Eric C., Shadid, John N., Kramer, Richard Michael Jack, Phillips, Edward Geoffrey, Conde, Sidafa, and Pawlowski, Roger P. IMEX and exact sequence discretization of the multi-fluid plasma model. United States: N. p., 2019.
Web. doi:10.1016/j.jcp.2019.05.052.
Miller, Sean T., Cyr, Eric C., Shadid, John N., Kramer, Richard Michael Jack, Phillips, Edward Geoffrey, Conde, Sidafa, & Pawlowski, Roger P. IMEX and exact sequence discretization of the multi-fluid plasma model. United States. https://doi.org/10.1016/j.jcp.2019.05.052
Miller, Sean T., Cyr, Eric C., Shadid, John N., Kramer, Richard Michael Jack, Phillips, Edward Geoffrey, Conde, Sidafa, and Pawlowski, Roger P. Tue .
"IMEX and exact sequence discretization of the multi-fluid plasma model". United States. https://doi.org/10.1016/j.jcp.2019.05.052. https://www.osti.gov/servlets/purl/1559495.
@article{osti_1559495,
title = {IMEX and exact sequence discretization of the multi-fluid plasma model},
author = {Miller, Sean T. and Cyr, Eric C. and Shadid, John N. and Kramer, Richard Michael Jack and Phillips, Edward Geoffrey and Conde, Sidafa and Pawlowski, Roger P.},
abstractNote = {Multi-fluid plasma models, where an electron fluid is modeled in addition to multiple ion and neutral species as well as the full set of Maxwell's equations, are useful for representing physics beyond the scope of classic MHD. This advantage presents challenges in appropriately dealing with electron dynamics and electromagnetic behavior characterized by the plasma and cyclotron frequencies and the speed of light. For physical systems, such as those near the MHD asymptotic regime, this requirement drastically increases runtimes for explicit time integration even though resolving fast dynamics may not be critical for accuracy. Implicit time integration methods, with efficient solvers, can help to step over fast time-scales that constrain stability, but do not strongly influence accuracy. As an extension, Implicit-explicit (IMEX) schemes provide an additional mechanism to choose which dynamics are evolved using an expensive implicit solve or resolved using a fast explicit solve. In this study, in addition to IMEX methods we also consider a physics compatible exact sequence spatial discretization. Here, this combines nodal bases (H-Grad) for fluid dynamics with a set of vector bases (H-Curl and H-Div) for Maxwell's equations. This discretization allows for multi-fluid plasma modeling without violating Gauss' laws for the electric and magnetic fields. This initial study presents a discussion of the major elements of this formulation and focuses on demonstrating accuracy in the linear wave regime and in the MHD limit for both a visco-resistive and a dispersive ideal MHD problem.},
doi = {10.1016/j.jcp.2019.05.052},
journal = {Journal of Computational Physics},
number = ,
volume = 397,
place = {United States},
year = {Tue Jul 23 00:00:00 EDT 2019},
month = {Tue Jul 23 00:00:00 EDT 2019}
}
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Figures / Tables:
Figure 1: Representation of the relationships between the spaces associated with the exact sequence discretization. Note how the derivative operators ∇, ∇x and ∇• map from one space to another, and that the gray area represents the null-space of the associated operator as described in Eq. (26). The discrete versionmore »
Figures / Tables found in this record: