TITLE

# A Fourth-Order-Centered Finite-Volume Scheme for Regular Hexagonal Grids

AUTHOR(S)
Miura, Hiroaki
PUB. DATE
December 2007
SOURCE
Monthly Weather Review;Dec2007, Vol. 135 Issue 12, p4030
SOURCE TYPE
DOC. TYPE
Article
ABSTRACT
Fourth-order-centered operators on regular hexagonal grids with the ZM-grid arrangement are described. The finite-volume method is used and operators are defined at hexagonal cell centers. The gradient operator is calculated from 12 surrounding cell center scalars. The divergence operator is defined from 12 surrounding cell corner vectors. A linear combination of local or interpolated values generates cell corner values used to calculate the operators. The flux-divergence operator applies the same cell corner values as those used in the gradient and divergence operators. The fourth-order convergence of the gradient and divergence operators is obtained in numerical tests using sufficiently smooth and differentiable test functions. The flux-divergence operator is formally second-order accurate. However, the results from a cone advection test show that the flux-divergence operator performs better than a commonly used second-order flux-divergence operator. Numerical dispersion and phase error are small because mean wind advection is computed with fourth-order accuracy.
ACCESSION #
28028609

## Related Articles

• Dust Lofting and Ingestion by Supercell Storms. Seigel, Robert B.; van den Heever, Susan C. // Journal of the Atmospheric Sciences;May2012, Vol. 69 Issue 5, p1453

Recent research pertaining to aerosol impacts on cloud microphysics has shown a need for understanding mineral dust entrainment into moist convection. The goal of this study is to examine the pathways in which nonmicrophysically active mineral dust is entrained into supercell storms within three...

• Evaluating Low-Cloud Simulation from an Upgraded Multiscale Modeling Framework Model. Part I: Sensitivity to Spatial Resolution and Climatology. Xu, Kuan-Man; Cheng, Anning // Journal of Climate;Aug2013, Vol. 26 Issue 16, p5717

The multiscale modeling framework, which replaces traditional cloud parameterizations with a 2D cloud-resolving model (CRM) in each atmospheric column, is a promising approach to climate modeling. The CRM component contains an advanced third-order turbulence closure, helping it to better...

• Springâ€“summer climatological circulation in the upper layer in the region of Cape St. Vincent, Southwest Portugal Sánchez, Ricardo F.; Relvas, Paulo // ICES Journal of Marine Science / Journal du Conseil;Dec2003, Vol. 60 Issue 6, p1232

Geostrophic transport and hydrographic measurements derived from a historical database (1900â€“1998) were used to study the springâ€“summer mean circulation in the upper layer south and west of Cape St. Vincent, Southwest (SW) Portugal. The larger-scale circulation scheme is forced by...

• On the Convergence of Broyden-Like Methods. Argyros, Ioannis K. // Acta Mathematica Sinica;Nov2007, Vol. 23 Issue 11, p2087

The author provides a finer local as well as semilocal convergence analysis of a certain class of Broyden-like methods for solving equations containing a nondifferentiable term on the m-dimensional Euclidean space ( m â‰¥ 1 a natural number).

• ON THE TRANSCENDENCE OF INFINITE SUMS OF VALUES OF RATIONAL FUNCTIONS. N. SARADHA; R. TIJDEMAN // Journal of the London Mathematical Society;Jun2003, Vol. 67 Issue 3, p580

Convergent sums $T = {\sum}_{n=1}^{\infty} P(n)/Q(n)$ and $U = {\sum}_{n=1}^{\infty}(-1)^n P(n)/Q(n)$, where $P(X), Q(X) \in {\mathbb Q}[X]$, and $Q(X)$ has only simple rational roots, are investigated. Adhikari, Shorey and the authors have shown that ...

• A Hybrid Method for a Countable Family of Multivalued Maps, Equilibrium Problems, and Variational Inequality Problems. Watcharaporn Cholamjiak; Suthep Suantai // Discrete Dynamics in Nature & Society;2010, Special section p1

We introduce a new monotone hybrid iterative scheme for finding a common element of the set of common fixed points of a countable family of non expansive multi valued maps, the set of solutions of variational inequality problem, and the set of the solutions of the equilibrium problem in a...

• Theoretical Convergence Analysis of a General Divisionâ€“deletion Algorithm for Solving Global Search Problems. X. Yang; M. Sun // Journal of Global Optimization;Jan2007, Vol. 37 Issue 1, p27

Abstract??Presented in this paper is the prototype of a very general algorithm referred to as Division ? Deletion Algorithm (DDA) for solving the most general global search problem. Various necessary conditions, sufficient conditions, and necessary and sufficient conditions for the convergence...

• The Truncated q-Bernstein Polynomials in the Case q>1. Turan, Mehmet // Abstract & Applied Analysis;2014, p1

The truncated q-Bernstein polynomials Bn,m,q(f; x) n âˆˆ â„•, and m âˆˆ â„•0 emerge naturally when the q-Bernstein polynomials of functions vanishing in some neighbourhood of 0 are considered. In this paper, the convergence of the truncated q-polynomials on [0, 1] is studied. To...

• monotone convergence theorem (early 20th century) Mathematics.  // Dictionary of Theories;2002, p351

Information on the monotone convergence theorem is presented. The theorem was proved by French mathematician Henri-Leon Lebesgue for the case where the limit function is integrable. The theorem is an increasing sequence of non-integrable measurable functiond which converghes almost everywhere to...

Share