A global numerical model for shallow water flows on the cubed-sphere grid is proposed in this paper. The model is constructed by using the constrained interpolation profile/multi-moment finite volume method (CIP/MM FVM). Two kinds of moments, i.e. the point value (PV) and the volume-integrated average (VIA) are defined and independently updated in the present model by different numerical formulations. The Lax-Friedrichs upwind splitting is used to update the PV moment in terms of a derivative Riemann problem, and a finite volume formulation derived by integrating the governing equations over each mesh element is used to predict the VIA moment. The cubed-sphere grid is applied to get around the polar singularity and to obtain uniform grid spacing for a spherical geometry. Highly localized reconstruction in CIP/MM FVM is well suited for the cubed-sphere grid, especially in dealing with the discontinuity in the coordinates between different patches. The mass conservation is completely achieved over the whole globe. The numerical model has been verified by Williamson's standard test set for shallow water equation model on sphere. The results reveal that the present model is competitive to most existing ones.
The two-dimensional nonhydrostatic compressible dynamical core for the atmosphere has been developed by using a new nodal-type high-order conservative method, the so-called multimoment constrained finitevolume (MCV) method. Different from the conventional finite-volume method, the predicted variables (unknowns) in an MCV scheme are the values at the solution points distributed within each mesh cell. The time evolution equations to update the unknown point values are derived from a set of constraint conditions based on the multimoment concept, where the constraint on the volume-integrated average (VIA) for each mesh cell is cast into a flux form and thus guarantees rigorously the numerical conservation. Two important features make the MCV method particularly attractive as an accurate and practical numerical framework for atmospheric and oceanic modeling. 1) The predicted variables are the nodal values at the solution points that can be flexibly located within a mesh cell (equidistant solution points are used in the present model). It is computationally efficient and provides great convenience in dealing with complex geometry and source terms. 2) High-order and physically consistent formulations can be built by choosing proper constraints in view of not only numerical accuracy and efficiency but also underlying physics. In this paper the authors present a dynamical core that uses the third-and the fourth-order MCV schemes. They have verified the numerical outputs of both schemes by widely used standard benchmark tests and obtained competitive results. The present numerical core provides a promising and practical framework for further development of nonhydrostatic compressible atmospheric models.
In this study, supercritical carbon dioxide extraction of ethyl p-methoxycinnamate from Kaempferia galanga L. rhizome and its apoptotic induction in human HepG2 cells are reported for the first time. By using supercritical carbon dioxide extraction, the yield of ethyl p-methoxycinnamate identified by gas chromatography mass spectrometry (GC-MS) was as high as 2.5% with respect to the raw materials. In the anticancer assay, it was found that ethyl p-methoxycinnamate could inhibit the proliferation of the human hepatocellular liver carcinoma HepG2 cell line in a dose-dependent manner and induce the significant increase of the subG0 cell population. After treatment with ethyl p-methoxycinnamate, phosphatidylserine of HepG2 cells could significantly translocate to the surface of the membrane. The increase of an early apoptotic population was observed by both annexin-fluorescein isothiocyanate (FITC) and propidium iodide (PI) staining. It was concluded that ethyl p-methoxycinnamate not only induced cells to enter into apoptosis, but also affected the progress of the cell cycle.
By using CSL3 multimoment interpolation, a piecewise cubic polynomial for spatial reconstruction can be obtained with four multimoment constraint conditions consisting of two point values at cell boundaries, one volume-integrated average and one slope parameter at the cell center. The resulting multimoment finite-volume scheme is of fourth-order accuracy. A non-oscillatory scheme can be derived by designing the proper formula to calculate the slope parameter at the cell center. A new strategy was recently proposed, using the Weighted Essentially Non-Oscillatory (WENO) concept to determine the slope parameter. Using a WENO-type limiter, the multimoment reconstruction can effectively remove nonphysical oscillations while keeping fourth-order accuracy in smooth regions. In this study, a WENO-type slope limiter is proposed and implemented in our multimoment finite-volume global transport model based on the cubed-sphere grid. The widely used benchmark tests, including both solid rotation and complicated deformational advection cases, are checked to verify the performance of the proposed global transport model. Numerical results reveal that a WENO-type slope limiter can greatly improve the accuracy of the multimoment finite-volume model compared with the former Total Variation Diminishing (TVD)-type limiter. Furthermore, the proposed limiter is constructed over a compact stencil of only three adjacent cells. Without any user-defined or problem-dependent parameters, the present model is very promising for practical applications. KEYWORDS cubed-sphere grid; global model; multimoment scheme; slope limiter; transport model; WENO
INTRODUCTIONDue to polar problems on the latitude-longitude grid, global computational meshes with a quasi-uniform grid spacing and free of polar problems, such as the cubed-sphere grid (Sadourny, 1972), icosahedral grid (Sadourny et al., 1968;Williamson, 1968), and yin-yang grid (Kageyama and Sato, 2004), are becoming popular in constructing global models, especially for those aiming at very high-resolution simulations of atmospheric dynamics. One of the key issues in implementing research and operational models on these quasi-uniform grids is the relatively complex grid structure, which causes essential difficulties in constructing high-order models and introduces extra grid-imprinting errors. In the past decade, some accurate global models have been proposed on these grids through the application of so-called "local" schemes, such as the discontinuous Galerkin scheme (Nair et al., 2005a;2005b), the spectral element scheme (Dennis et al., 2012), the multimoment scheme (Chen et al., 2014) and so on. These schemes are accomplished based on compact stencils (usually within a single computational element) and are very convenient to implement in spherical geometry to develop high-order models. Furthermore, these schemes are computationally intensive, so they are highly scalable on massively parallel clusters. A comprehensive review on the applications of quasi-uniform grids can be found in the work of...
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