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

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.
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  1. Los Alamos National Lab. (LANL), Los Alamos, NM (United States). Center for Nonlinear Studies (CNLS)
Publication Date:
Report Number(s):
Journal ID: ISSN 0021-9991; TRN: US1800373
Grant/Contract Number:
Accepted Manuscript
Journal Name:
Journal of Computational Physics
Additional Journal Information:
Journal Volume: 348; Journal Issue: C; Journal ID: ISSN 0021-9991
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)
Country of Publication:
United States
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; arbitrary order; general polygonal; general polyhedral; mimetic finite difference; non-symmetric diffusion; hall effect; resistive magnetohydrodynamics
OSTI Identifier: