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Title: A Low Order Mimetic Finite Difference Method for Resistive Magnetohydrodynamics in 2D

Abstract

We developed a low order Mimetic Finite Difference (MFD) discretization for the equations of magnetohydrodynamics (MHD) in two space dimensions. These equations describe the evolution of the electric and magnetic fields in the presence of prescribed velocity field.The method is designed to work on general polygonal meshes and preserves the divergence-free condition on the magnetic field. The electric field is discretized at the vertices/nodes and the magnetic field uses edge-based discretization. The method reconstructs the magnetic field to extract nodal values necessary to approximate some terms present in Ohm’s law. We test the robustness of our numerical scheme on three different types of meshes: with triangular elements, quadrilateral and unstructured polyhedrons obtain from a Voronoi tesselation. Analysis of the convergence for each of the aforementioned mesh types is presented. We finish with a test problem that shows the method is capable of modelling magnetic reconnection.

Authors:
 [1];  [1]
  1. Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Publication Date:
Research Org.:
Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Sponsoring Org.:
National Science Foundation (NSF); USDOE
OSTI Identifier:
1473774
Report Number(s):
LA-UR-18-29007
DOE Contract Number:  
AC52-06NA25396
Resource Type:
Technical Report
Country of Publication:
United States
Language:
English
Subject:
mimetic finite difference; resistive magnetohydrodynamics

Citation Formats

Naranjo, Sebastian, and Gyrya, Vitaliy. A Low Order Mimetic Finite Difference Method for Resistive Magnetohydrodynamics in 2D. United States: N. p., 2018. Web. doi:10.2172/1473774.
Naranjo, Sebastian, & Gyrya, Vitaliy. A Low Order Mimetic Finite Difference Method for Resistive Magnetohydrodynamics in 2D. United States. doi:10.2172/1473774.
Naranjo, Sebastian, and Gyrya, Vitaliy. Fri . "A Low Order Mimetic Finite Difference Method for Resistive Magnetohydrodynamics in 2D". United States. doi:10.2172/1473774. https://www.osti.gov/servlets/purl/1473774.
@article{osti_1473774,
title = {A Low Order Mimetic Finite Difference Method for Resistive Magnetohydrodynamics in 2D},
author = {Naranjo, Sebastian and Gyrya, Vitaliy},
abstractNote = {We developed a low order Mimetic Finite Difference (MFD) discretization for the equations of magnetohydrodynamics (MHD) in two space dimensions. These equations describe the evolution of the electric and magnetic fields in the presence of prescribed velocity field.The method is designed to work on general polygonal meshes and preserves the divergence-free condition on the magnetic field. The electric field is discretized at the vertices/nodes and the magnetic field uses edge-based discretization. The method reconstructs the magnetic field to extract nodal values necessary to approximate some terms present in Ohm’s law. We test the robustness of our numerical scheme on three different types of meshes: with triangular elements, quadrilateral and unstructured polyhedrons obtain from a Voronoi tesselation. Analysis of the convergence for each of the aforementioned mesh types is presented. We finish with a test problem that shows the method is capable of modelling magnetic reconnection.},
doi = {10.2172/1473774},
journal = {},
number = ,
volume = ,
place = {United States},
year = {2018},
month = {9}
}

Technical Report:

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