Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
6930825 | Journal of Computational Physics | 2016 | 16 Pages |
Abstract
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(kâ
); the derived (dual) mimetic operator approximates ââ(â
). 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 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.
Related Topics
Physical Sciences and Engineering
Computer Science
Computer Science Applications
Authors
Konstantin Lipnikov, Gianmarco Manzini, J. David Moulton, Mikhail Shashkov,