The arbitrary order mimetic finite difference method for a diffusion equation with a non-symmetric diffusion tensor
| Autor: | Vitaliy Gyrya, Konstantin Lipnikov |
|---|---|
| Rok vydání: | 2017 |
| Předmět: |
Numerical Analysis
Diffusion equation Physics and Astronomy (miscellaneous) Discretization Applied Mathematics Mathematical analysis Finite difference method Finite difference 010103 numerical & computational mathematics Mass matrix 01 natural sciences Computer Science Applications 010101 applied mathematics Computational Mathematics Positive definiteness Rate of convergence Modeling and Simulation 0101 mathematics Diffusion (business) Mathematics |
| Zdroj: | Journal of Computational Physics. 348:549-566 |
| ISSN: | 0021-9991 |
| DOI: | 10.1016/j.jcp.2017.07.019 |
| Popis: | 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 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. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|
Full Text from ScienceDirect