The mimetic finite difference method for elliptic and parabolic problems with a staggered discretization of diffusion coefficient
- Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Numerical schemes for nonlinear parabolic equations based on the harmonic averaging of cell-centered diffusion coefficients break down when some of these coefficients go to zero or their ratio grows. To tackle this problem, we propose new mimetic finite difference schemes that use a staggered discretization of the diffusion coefficient. The primary mimetic operator approximates div (k•); the derived (dual) mimetic operator approximates - ∇(•). The new mimetic schemes preserve symmetry and positive-definiteness of the continuum problem which allows us to use algebraic solvers with optimal complexity. We perform detailed numerical analysis of the new schemes for linear elliptic problems and a specially designed linear parabolic problem that has solution dynamics typical for nonlinear problems. We also show that the new schemes are competitive with the state-of-the-art schemes for steady-state problems but provide much more accurate solution dynamics for the transient problem.
- Research Organization:
- Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)
- Sponsoring Organization:
- USDOE National Nuclear Security Administration (NNSA); USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR)
- Grant/Contract Number:
- AC52-06NA25396
- OSTI ID:
- 1457241
- Alternate ID(s):
- OSTI ID: 1397677
- Report Number(s):
- LA-UR-15-23755; TRN: US1901324
- Journal Information:
- Journal of Computational Physics, Vol. 305, Issue C; ISSN 0021-9991
- Publisher:
- ElsevierCopyright Statement
- Country of Publication:
- United States
- Language:
- English
Web of Science
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