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

Gyrya, V.; Lipnikov, K.

doi:10.1016/j.jcp.2017.07.019

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

Journal Article · Tue Jul 18 00:00:00 EDT 2017 · Journal of Computational Physics

DOI:https://doi.org/10.1016/j.jcp.2017.07.019· OSTI ID:1412852

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Los Alamos National Lab. (LANL), Los Alamos, NM (United States). Center for Nonlinear Studies (CNLS)

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.

View Accepted Manuscript (DOE)

Research Organization:: Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

Sponsoring Organization:: USDOE Office of Science (SC). Advanced Scientific Computing Research (ASCR) (SC-21)

Grant/Contract Number:: AC52-06NA25396

OSTI ID:: 1412852

Alternate ID(s):: OSTI ID: 1549594

Report Number(s):: LA-UR--16-27864

Journal Information:: Journal of Computational Physics, Journal Name: Journal of Computational Physics Journal Issue: C Vol. 348; ISSN 0021-9991

Publisher:: ElsevierCopyright Statement

Country of Publication:: United States

Language:: English

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71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
arbitrary order
general polygonal
general polyhedral
hall effect
mimetic finite difference
non-symmetric diffusion
resistive magnetohydrodynamics

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

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