A Multimoment Finite-Volume Shallow-Water Model on the Yin–Yang Overset Spherical Grid

Abstract

A numerical model for shallow-water equations has been built and tested on the Yin-Yang overset spherical grid. A high-order multimoment finite-volume method is used for the spatial discretization in which two kinds of so-called moments of the physical field [i.e., the volume integrated average (VIA) and the point value (PV)] are treated as the model variables and updated separately in time. In the present model, the PV is computed by the semi-implicit semi-Lagrangian formulation, whereas the VIA is predicted in time via a flux-based finite-volume method and is numerically conserved on each component grid. The concept of including an extra moment (i.e., the volume-integrated value) to enforce the numerical conservativeness provides a general methodology and applies to the existing semi-implicit semi-Lagrangian formulations. Based on both VIA and PV, the high-order interpolation reconstruction can only be done over a single grid cell, which then minimizes the overlapping zone between the Yin and Yang components and effectively reduces the numerical errors introduced in the interpolation required to communicate the data between the two components. The present model completely gets around the singularity and grid convergence in the polar regions of the conventional longitude-latitude grid. Being an issue demanding further investigation, the high-order interpolation across the overlapping region of the Yin-Yang grid in the current model does not rigorously guarantee the numerical conservativeness. Nevertheless, these numerical tests show that the global conservation error in the present model is negligibly small. The model has competitive accuracy and efficiency.

Experiments with different discretizations for the shallow‐water equations on a sphere

“…In general, we use a grid with fixed resolution and the analysis of meshrefinement techniques discussed by St-Cyr et al (2008) and Weller et al (2009) is not included. We expect that the results presented here will complement recent experiments with finite-volume and discontinuous Galerkin schemes on an icosahedral grid (Läuter et al, 2008;Walko and Avissar, 2008;Bernard et al, 2009;Lee and MacDonald, 2009;Ii and Xiao, 2010), on a cubed-sphere grid Nair, 2009) and on a Yin-Yang grid (Li et al, 2008). This article is organized as follows.…”

The ICON-1.2 hydrostatic atmospheric dynamical core on triangular grids – Part 1: Formulation and performance of the baseline version

“…The efforts of Heikes and Randall (1995a,b), Ringler and Randall (2002), Majewski et al (2002), Tomita and Satoh (2004) and Giraldo and Rosmond (2004) are examples that developed models on icosahedral grids. Other grid configurations such as the cubed sphere (e.g., McGregor, 1996;Giraldo et al, 2003;Putman and Lin, 2007), Yin-Yang grid (e.g., Kageyama and Sato, 2004;Qaddouri et al, 2008;Li et al, 2007), and Fibonacci grid (Swinbank and Purser, 2006), have also been investigated. The numerical discretizations applied in these models include not only finite-difference and finite-volume schemes (e.g., Heikes and Randall, 1995a;Putman and Lin, 2007), but also modern techniques such as high-order continuous and discontinuous Galerkin methods (e.g.…”

An Adaptive Multimoment Global Model on a Cubed Sphere

“…Shown in the existing studies Ii and Xiao (2007), Akoh et al (2008), Chen and Xiao (2008), Li et al (2008), Xiao (2009, 2010), and Akoh et al (2010), the multimoment schemes show competitive performance in respect to computational accuracy, efficiency, robustness, and flexibility. The increased degrees of freedom (DOFs) by using the multimoment concept especially make it possible to use compact stencil for high-order spatial reconstruction compared with the single moment method (e.g., conventional finite difference-volume method).…”