Time-discretization of a plasma-neutral MHD model with a semi-implicit leapfrog algorithm

Taheri, Sina; King, Jacob R; Shumlak, Uri

doi:10.1016/j.cpc.2022.108288

Time-discretization of a plasma-neutral MHD model with a semi-implicit leapfrog algorithm

Journal Article · Wed Jan 12 23:00:00 EST 2022 · Computer Physics Communications

DOI:https://doi.org/10.1016/j.cpc.2022.108288· OSTI ID:1843847

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Univ. of Washington, Seattle, WA (United States); Tech-X Corporation
Tech-X Corporation, Boulder, CO (United States)
Univ. of Washington, Seattle, WA (United States)

The semi-implicit leapfrog time-discretization is a workhorse algorithm for initial-value MHD codes to bridge between vastly separated time scales. Inclusion of atomic interactions with neutrals breaks the functional structure of the MHD equations that exploited by the leapfrog. In this work, we address how to best integrate atomic physics into the semi-implicit leapfrog. Following the Crank-Nicolson method, one approach is to time-center the atomic interactions in the linear solver and use a Newton method to include the nonlinear contributions. Alternatively, another family of methods are based on operator-splitting the terms associated with the atomic interactions using a Strang-splitting technique. These methods naturally break equations into constituent ODE and PDE parts and preserve the structure exploited by the semi-implicit leapfrog. We study the accuracy and efficiency of these methods through a battery of 0D and 1D cases and show that a second-order-in-time Douglas-Rachford inspired coupling between the ODE and PDE advances is effective in reducing the time-discretization error to be comparable to that of Crank-Nicolson with Newton iteration of the nonlinear terms. Splitting ODE and PDE parts results in independent matrix solves for each field which reduces the computational cost considerably and provides parallelization over species relative to Crank-Nicolson.

View Accepted Manuscript (DOE)

Research Organization:: Tech X Corporation, Boulder, CO (United States)

Sponsoring Organization:: USDOE Office of Science (SC)

Grant/Contract Number:: SC0018311; SC0016256

OSTI ID:: 1843847

Alternate ID(s):: OSTI ID: 1840819

Journal Information:: Computer Physics Communications, Journal Name: Computer Physics Communications Vol. 274; ISSN 0010-4655

Publisher:: ElsevierCopyright Statement

Country of Publication:: United States

Language:: English

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