A non‐oscillatory multimoment finite‐volume global transport model on a cubed‐sphere grid using the WENO slope limiter

Quart J Royal Meteoro Soc

et al. 2019

Self Cite

An oscillation‐less multimoment global transport model was proposed by Tang et al. in 2018 by introducing a slope limiter based on the weighted essentially non‐oscillatory (WENO) concept. The spurious oscillations around the discontinuities and strong gradients can be effectively removed and the model preserves the fourth‐order accuracy in spherical geometry for smooth solutions. However, the WENO limiter does not strictly guarantee the non‐negativity of numerical solution and the resulting model will violate the physical principle due to the existence of the nonphysical negative undershoots. As the numerical fluxes, which determine the time tendency of the volume‐integrated average, are evaluated by the point values (PVs) defined along the cell boundaries in the multimoment finite‐volume schemes, the non‐negativity preserving model can be accomplished by modifying those PVs to implement the corrections on the numerical fluxes proposed in the positive definite flux‐corrected transport (FCT) method by Smolarkiewicz in 1989. In this study, a non‐negativity correction algorithm is proposed for a global transport model using the MM‐FVM_WENO scheme and verified by simulating the widely used benchmark tests.

Section: Numerical Tests and Resultsmentioning

confidence: 99%

Section: Numerical Tests and Resultsmentioning

confidence: 99%

“…of Tang et al . (). The time tendency of the VIA for a Cartesian grid cell,

{scriptC}_{italicij}

, is

δ {normalℳ}_{italicij} = - \frac{1}{Δ x Δ y} (E_{i + \frac{1}{2} j} - E_{i - \frac{1}{2} j} + F_{ij + \frac{1}{2}} - F_{ij - \frac{1}{2}}),

where Δ x , Δ y are grid spacing in x ‐ and y ‐directions, E and F are line‐integrated values of flux functions along boundary edges and evaluated by 3‐point Simpson's rule as

E_{i \pm \frac{1}{2} j} = \frac{Δ y}{6} (e_{i \pm \frac{1}{2} j - \frac{1}{2}} + 4 e_{i \pm \frac{1}{2} j} + e_{i \pm \frac{1}{2} j + \frac{1}{2}})

and

F_{ij \pm \frac{1}{2}} = \frac{Δ x}{6} (f_{i - \frac{1}{2} j \pm \frac{1}{2}} + 4 f_{ij \pm \frac{1}{2}} + f_{i + \frac{1}{2} j \pm \frac{1}{2}}) .

…”

Section: Extension To Two‐dimensional Case and Global Transport Modelmentioning

confidence: 99%

Section: Non-negativity Correction Algorithm In the One-dimensional Casementioning

confidence: 99%

“…In the two-dimensional case, the configuration of DOFs is shown in Fig. 4 of Tang et al (2018). The time tendency of the VIA for a Cartesian grid cell,  , is…”

Section: Extension To Two-dimensional Case and Global Transport Modelmentioning

confidence: 99%

See 3 more Smart Citations

A note on non‐negativity correction for a multimoment finite‐volume transport model with WENO limiter

Shen

Quart J Royal Meteoro Soc

et al. 2019

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A nonnegative and shape‐preserving global transport model on cubed sphere using high‐order conservative collocation scheme

Huang

Numerical Methods in Fluids

et al. 2021

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A numerical model for global tracer transport is implemented by using Gauss–Legendre‐point conservative collocation (GLPCC) scheme on cubed sphere. Three‐point GLPCC scheme can achieve fifth‐order accuracy in the spherical geometry. To remove the spurious oscillations in the regions with strong gradients or discontinuities, the hierarchical reconstruction (HR) is applied to the “troubled cells” identified by a smoothness indicator based on the WENO concept. To assure the positivity‐preserving property, a flux correction operation is adopted to impose the restriction on the mass reduction due to the fluxes leaving the cell edges. The proposed numerical scheme aims to remove the nonphysical oscillations while preserving the accuracy in the smooth regions and maintain the compact spatial stencil as far as possible by making full use of degrees of freedom. The proposed schemes are evaluated by simulating the widely used benchmark tests for advection equation in one dimension and multidimensions of spherical geometry. Numerical results show that the fifth‐order accuracy is well preserved for smooth problems, while numerical oscillations can be effectively removed and the nonnegativity of the solutions is strictly guaranteed. It is very promising to develop the practical numerical model for tracer transport computation in atmospheric general circulation models using the proposed numerical framework.

A three‐dimensional positivity‐preserving and conservative multimoment finite‐volume transport model on a cubed‐sphere grid

Tang

Quart J Royal Meteoro Soc

Shen

et al. 2022

Self Cite

A three‐dimensional positivity‐preserving and conservative transport model on a cubed‐sphere grid is presented using a multimoment finite‐volume (MMFV) method. The three‐point fourth‐order MMFV method with boundary gradient switching projection is utilized to ensure nonoscillatory numerical solutions in the horizontal, while the simple and computationally efficient semi‐Lagrangian piecewise rational method is used to allow a large time step in the vertical. By means of horizontal and vertical separation, a Strang‐type splitting technique is adopted to advance the numerical solutions in time. Non‐negative corrections are made to achieve positive‐definite preservation exactly. The resulting transport model is inherently conservative, high‐accuracy, and positive‐definite, and allows a large Courant number no matter how dense the vertical grid is. Various benchmark test cases, including three representative advection tests and an idealized terminator chemistry test, are conducted to validate the performance of the model presented. The numerical results indicate that the model is quite competitive in comparison with the existing models in the literature and looks very promising in real atmospheric simulations.