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Title: The arbitrary order mimetic finite difference method for a diffusion equation with a non-symmetric diffusion tensor

Abstract

Here, we present the arbitrary order mimetic finite difference (MFD) discretization for the diffusion equation with non-symmetric tensorial diffusion coefficient in a mixed formulation on general polygonal meshes. The diffusion tensor is assumed to be positive definite. The asymmetry of the diffusion tensor requires changes to the standard MFD construction. We also present new approach for the construction that guarantees positive definiteness of the non-symmetric mass matrix in the space of discrete velocities. The numerically observed convergence rate for the scalar quantity matches the predicted one in the case of the lowest order mimetic scheme. For higher orders schemes, we observed super-convergence by one order for the scalar variable which is consistent with the previously published result for a symmetric diffusion tensor. The new scheme was also tested on a time-dependent problem modeling the Hall effect in the resistive magnetohydrodynamics.

Authors:
ORCiD logo [1]; ORCiD logo [1]
  1. Los Alamos National Lab. (LANL), Los Alamos, NM (United States). Center for Nonlinear Studies (CNLS)
Publication Date:
Research Org.:
Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Sponsoring Org.:
USDOE Office of Science (SC). Advanced Scientific Computing Research (ASCR) (SC-21); USDOE National Nuclear Security Administration (NNSA); USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR)
OSTI Identifier:
1412852
Alternate Identifier(s):
OSTI ID: 1549594
Report Number(s):
LA-UR-16-27864
Journal ID: ISSN 0021-9991; TRN: US1800373
Grant/Contract Number:  
AC52-06NA25396
Resource Type:
Journal Article: Accepted Manuscript
Journal Name:
Journal of Computational Physics
Additional Journal Information:
Journal Volume: 348; Journal Issue: C; Journal ID: ISSN 0021-9991
Publisher:
Elsevier
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; arbitrary order; general polygonal; general polyhedral; mimetic finite difference; non-symmetric diffusion; hall effect; resistive magnetohydrodynamics

Citation Formats

Gyrya, V., and Lipnikov, K. The arbitrary order mimetic finite difference method for a diffusion equation with a non-symmetric diffusion tensor. United States: N. p., 2017. Web. doi:10.1016/j.jcp.2017.07.019.
Gyrya, V., & Lipnikov, K. The arbitrary order mimetic finite difference method for a diffusion equation with a non-symmetric diffusion tensor. United States. https://doi.org/10.1016/j.jcp.2017.07.019
Gyrya, V., and Lipnikov, K. Tue . "The arbitrary order mimetic finite difference method for a diffusion equation with a non-symmetric diffusion tensor". United States. https://doi.org/10.1016/j.jcp.2017.07.019. https://www.osti.gov/servlets/purl/1412852.
@article{osti_1412852,
title = {The arbitrary order mimetic finite difference method for a diffusion equation with a non-symmetric diffusion tensor},
author = {Gyrya, V. and Lipnikov, K.},
abstractNote = {Here, we present the arbitrary order mimetic finite difference (MFD) discretization for the diffusion equation with non-symmetric tensorial diffusion coefficient in a mixed formulation on general polygonal meshes. The diffusion tensor is assumed to be positive definite. The asymmetry of the diffusion tensor requires changes to the standard MFD construction. We also present new approach for the construction that guarantees positive definiteness of the non-symmetric mass matrix in the space of discrete velocities. The numerically observed convergence rate for the scalar quantity matches the predicted one in the case of the lowest order mimetic scheme. For higher orders schemes, we observed super-convergence by one order for the scalar variable which is consistent with the previously published result for a symmetric diffusion tensor. The new scheme was also tested on a time-dependent problem modeling the Hall effect in the resistive magnetohydrodynamics.},
doi = {10.1016/j.jcp.2017.07.019},
url = {https://www.osti.gov/biblio/1412852}, journal = {Journal of Computational Physics},
issn = {0021-9991},
number = C,
volume = 348,
place = {United States},
year = {2017},
month = {7}
}

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Cited by: 1 work
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