@Article{IJNAM-14-419,
author = {},
title = {A Systematic Method to Construct Mimetic Finite-Difference Schemes for Incompressible Flows},
journal = {International Journal of Numerical Analysis and Modeling},
year = {2017},
volume = {14},
number = {3},
pages = {419--436},
abstract = {<p style="text-align: justify;">We present a general procedure to construct a non-linear mimetic finite-difference
operator. The method is very simple and general: it can be applied for any order scheme, for any
number of grid points and for any operator constraints.<br/>In order to validate the procedure, we apply it to a specific example, the Jacobian operator
for the vorticity equation. In particular we consider a finite difference approximation of a second
order Jacobian which uses a 9$\times$9 uniform stencil, verifies the skew-symmetric property and satisfies
physical constraints such as conservation of energy and enstrophy. This particular choice has been
made in order to compare the present scheme with Arakawa&#39;s renowned Jacobian, which turns out
to be a specific case of the general solution. Other possible generalizations of Arakawa&#39;s Jacobian
are available in literature but only the present approach ensures that the class of solutions found is
the widest possible. A simplified analysis of the general scheme is proposed in terms of truncation
error and study of the linearised operator together with some numerical experiments. We also
propose a class of analytical solutions for the vorticity equation to compare an exact solution with
our numerical results.</p>},
issn = {2617-8710},
doi = {https://doi.org/},
url = {http://global-sci.org/intro/article_detail/ijnam/10015.html}
}