Abstract
A positivity-preserving conservative semi-Lagrangian transport model by multi-moment finite volume method has been developed on the cubed-sphere grid. Two kinds of moments (i.e., point values (PV moment) at cell interfaces and volume integrated average (VIA moment) value) are defined within a single cell. The PV moment is updated by a conventional semi-Lagrangian method, while the VIA moment is cast by the flux form formulation to assure the exact numerical conservation. Different from the spatial approximation used in the CSL2 (conservative semi-Lagrangian scheme with second order polynomial function) scheme, a monotonic rational function which can effectively remove non-physical oscillations is reconstructed within a single cell by the PV moments and VIA moment. To achieve exactly positive-definite preserving, two kinds of corrections are made on the original conservative semi-Lagrangian with rational function (CSLR) scheme. The resulting scheme is inherently conservative, non-negative, and allows a Courant number larger than one. Moreover, the spatial reconstruction can be performed within a single cell, which is very efficient and economical for practical implementation. In addition, a dimension-splitting approach coupled with multi-moment finite volume scheme is adopted on cubed-sphere geometry, which benefitsthe implementation of the 1D CSLR solver with large Courant number. The proposed model is evaluated by several widely used benchmark tests on cubed-sphere geometry. Numerical results show that the proposed transport model can effectively remove nonphysical oscillations and preserve the numerical non-negativity, and it has the potential to transport the tracers accurately in a real atmospheric model.
Highlights
IntroductionGlobal advection transport describes the motion of various passive tracers in the atmosphere, which is a basic pro-
Global advection transport describes the motion of various passive tracers in the atmosphere, which is a basic pro- TANG ET AL.weak singularities, such as the cubed-sphere grid, Yin-Yang grid, and icosahedral grid are becoming more and more popular in developing global transport models
A non-negativity and conservative semi-Lagrangian transport scheme based on a multi-moment finite volume method has been developed on the cubed-sphere grid
Summary
Global advection transport describes the motion of various passive tracers in the atmosphere, which is a basic pro-. Nakamura et al (2001) proposed a flux-form FVSL method based on their previous Constrained Interpolation Profile (CIP) scheme (Yabe and Aoki, 1991), calling it CIPCSL. In their method, the point values at cell boundaries and the cell-averaged value are used to reconstruct the piecewise interpolation profile. The semi-Lagrangian approach permits a large time step, and the flux-form formulation of updating cell-average values makes the scheme inherently conservative in terms of cell-integrated average values. We make some modifications on the CSLR scheme to make it non-negative and extend it to the cubedsphere grid to develop a global transport model.
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