A 3D compressible nonhydrostatic dynamic core based on a three-point multi-moment constrained finite-volume (MCV) method is developed by extending the previous 2D nonhydrostatic atmospheric dynamics to 3D on a terrain...A 3D compressible nonhydrostatic dynamic core based on a three-point multi-moment constrained finite-volume (MCV) method is developed by extending the previous 2D nonhydrostatic atmospheric dynamics to 3D on a terrainfollowing grid. The MCV algorithm defines two types of moments: the point-wise value (PV) and the volume-integrated average (VIA). The unknowns (PV values) are defined at the solution points within each cell and are updated through the time evolution formulations derived from the governing equations. Rigorous numerical conservation is ensured by a constraint on the VIA moment through the flux form formulation. The 3D atmospheric dynamic core reported in this paper is based on a three-point MCV method and has some advantages in comparison with other existing methods, such as uniform third-order accuracy, a compact stencil, and algorithmic simplicity. To check the performance of the 3D nonhydrostatic dynamic core, various benchmark test cases are performed. All the numerical results show that the present dynamic core is very competitive when compared to other existing advanced models, and thus lays the foundation for further developing global atmospheric models in the near future.展开更多
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 interface...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 1 D 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 nonnegativity,and it has the potential to transport the tracers accurately in a real atmospheric model.展开更多
With an increase in model resolution,compact high-order numerical advection scheme can improve its effectiveness and competitiveness in oceanic modeling due to its high accuracy and scalability on massive-processor co...With an increase in model resolution,compact high-order numerical advection scheme can improve its effectiveness and competitiveness in oceanic modeling due to its high accuracy and scalability on massive-processor computers.To provide high-quality numerical ocean simulation on overset grids,we tried a novel formulation of the fourth-order multi-moment constrained finite volume scheme to simulate continuous and discontinuous problems in the Cartesian coordinate.Utilizing some degrees of freedom over each cell and derivatives at the cell center,we obtained a two-dimensional(2D)cubic polynomial from which point values on the extended overlap can achieve fourth-order accuracy.However,this interpolation causes a lack of conservation because the flux between the regions are no longer equal;thus,a flux correction is implemented to ensure conservation.A couple of numerical experiments are presented to evaluate the numerical scheme,which confirms its approximately fourth-order accuracy in conservative transportation on overset grid.The test cases reveal that the scheme is effective to suppress numerical oscillation in discontinuous problems,which may be powerful for salinity advection computing with a sharp gradient.展开更多
An adaptive 2 D nonhydrostatic dynamical core is proposed by using the multi-moment constrained finite-volume(MCV) scheme and the Berger-Oliger adaptive mesh refinement(AMR) algorithm. The MCV scheme takes several poi...An adaptive 2 D nonhydrostatic dynamical core is proposed by using the multi-moment constrained finite-volume(MCV) scheme and the Berger-Oliger adaptive mesh refinement(AMR) algorithm. The MCV scheme takes several pointwise values within each computational cell as the predicted variables to build high-order schemes based on single-cell reconstruction. Two types of moments, such as the volume-integrated average(VIA) and point value(PV), are defined as constraint conditions to derive the updating formulations of the unknowns, and the constraint condition on VIA guarantees the rigorous conservation of the proposed model. In this study, the MCV scheme is implemented on a height-based, terrainfollowing grid with variable resolution to solve the nonhydrostatic governing equations of atmospheric dynamics. The AMR grid of Berger-Oliger consists of several groups of blocks with different resolutions, where the MCV model developed on a fixed structured mesh can be used directly. Numerical formulations are designed to implement the coarsefine interpolation and the flux correction for properly exchanging the solution information among different blocks. Widely used benchmark tests are carried out to evaluate the proposed model. The numerical experiments on uniform and AMR grids indicate that the adaptive model has promising potential for improving computational efficiency without losing accuracy.展开更多
In this study,the adaption of a novel three-point multi-moment constrained finite-volume transport scheme for uniform points with center constraints(MCV3_UPCC)to cubed sphere geometry is implemented and described.For ...In this study,the adaption of a novel three-point multi-moment constrained finite-volume transport scheme for uniform points with center constraints(MCV3_UPCC)to cubed sphere geometry is implemented and described.For the MCV3_UPCC scheme,the three equidistant solution points are located within a single cell and a polynomial of 4th degree can be built by imposing the multi-moment center constraints.The resultant scheme has third-order accuracy and guarantees the exact numerical conservation.The Fourier analysis of MCV3_UPCC scheme demonstrates that the novel MCV3_UPCC has better numerical dissipation and dispersion than the original 3rd order Multi-moment Constrained finite Volume(MCV3)scheme.Then it is applied to quasi-uniform cubed-sphere grid,which is designed to avoid the polar problem on the traditional latitude–longitude grid.To suppress the non-physical numerical oscillations,a bound-preserving(BP)algorithm to constrain the conserved advected tracer to within the initial maximum and minimum values is also implemented.The scheme is validated with several widely used benchmarks involving prescribed non-divergent two-dimensional flow on the sphere and different initial tracer distributions.The resulting conservative transport model with high-order accuracy and positive preserving property is comparable to other high-order schemes and has the potential for the numerical simulation of various traces in the atmosphere.展开更多
基金supported by the National Key Research and Development Program of China (Grant Nos. 2017YFC1501901 and 2017YFA0603901)the Beijing Natural Science Foundation (Grant No. JQ18001)
文摘A 3D compressible nonhydrostatic dynamic core based on a three-point multi-moment constrained finite-volume (MCV) method is developed by extending the previous 2D nonhydrostatic atmospheric dynamics to 3D on a terrainfollowing grid. The MCV algorithm defines two types of moments: the point-wise value (PV) and the volume-integrated average (VIA). The unknowns (PV values) are defined at the solution points within each cell and are updated through the time evolution formulations derived from the governing equations. Rigorous numerical conservation is ensured by a constraint on the VIA moment through the flux form formulation. The 3D atmospheric dynamic core reported in this paper is based on a three-point MCV method and has some advantages in comparison with other existing methods, such as uniform third-order accuracy, a compact stencil, and algorithmic simplicity. To check the performance of the 3D nonhydrostatic dynamic core, various benchmark test cases are performed. All the numerical results show that the present dynamic core is very competitive when compared to other existing advanced models, and thus lays the foundation for further developing global atmospheric models in the near future.
基金supported by the National Key Research and Development Program of China (Grant Nos.2017YFC1501901 and 2017YFA0603901)the Beijing Natural Science Foundation (Grant No.JQ18001)。
文摘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 1 D 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 nonnegativity,and it has the potential to transport the tracers accurately in a real atmospheric model.
基金Dr.X.L.Li at the China Meteorological Administration.This study was supported by grants from the National Natural Science Foundation of China(Nos.41575103 and 91637210).
文摘With an increase in model resolution,compact high-order numerical advection scheme can improve its effectiveness and competitiveness in oceanic modeling due to its high accuracy and scalability on massive-processor computers.To provide high-quality numerical ocean simulation on overset grids,we tried a novel formulation of the fourth-order multi-moment constrained finite volume scheme to simulate continuous and discontinuous problems in the Cartesian coordinate.Utilizing some degrees of freedom over each cell and derivatives at the cell center,we obtained a two-dimensional(2D)cubic polynomial from which point values on the extended overlap can achieve fourth-order accuracy.However,this interpolation causes a lack of conservation because the flux between the regions are no longer equal;thus,a flux correction is implemented to ensure conservation.A couple of numerical experiments are presented to evaluate the numerical scheme,which confirms its approximately fourth-order accuracy in conservative transportation on overset grid.The test cases reveal that the scheme is effective to suppress numerical oscillation in discontinuous problems,which may be powerful for salinity advection computing with a sharp gradient.
基金supported by The National Key Research and Development Program of China(Grants Nos.2017YFA0603901 and 2017YFC1501901)The National Natural Science Foundation of China(Grant No.41522504)。
文摘An adaptive 2 D nonhydrostatic dynamical core is proposed by using the multi-moment constrained finite-volume(MCV) scheme and the Berger-Oliger adaptive mesh refinement(AMR) algorithm. The MCV scheme takes several pointwise values within each computational cell as the predicted variables to build high-order schemes based on single-cell reconstruction. Two types of moments, such as the volume-integrated average(VIA) and point value(PV), are defined as constraint conditions to derive the updating formulations of the unknowns, and the constraint condition on VIA guarantees the rigorous conservation of the proposed model. In this study, the MCV scheme is implemented on a height-based, terrainfollowing grid with variable resolution to solve the nonhydrostatic governing equations of atmospheric dynamics. The AMR grid of Berger-Oliger consists of several groups of blocks with different resolutions, where the MCV model developed on a fixed structured mesh can be used directly. Numerical formulations are designed to implement the coarsefine interpolation and the flux correction for properly exchanging the solution information among different blocks. Widely used benchmark tests are carried out to evaluate the proposed model. The numerical experiments on uniform and AMR grids indicate that the adaptive model has promising potential for improving computational efficiency without losing accuracy.
基金Supported by the National Natural Science Foundation of China(42275168 and 42105002)。
文摘In this study,the adaption of a novel three-point multi-moment constrained finite-volume transport scheme for uniform points with center constraints(MCV3_UPCC)to cubed sphere geometry is implemented and described.For the MCV3_UPCC scheme,the three equidistant solution points are located within a single cell and a polynomial of 4th degree can be built by imposing the multi-moment center constraints.The resultant scheme has third-order accuracy and guarantees the exact numerical conservation.The Fourier analysis of MCV3_UPCC scheme demonstrates that the novel MCV3_UPCC has better numerical dissipation and dispersion than the original 3rd order Multi-moment Constrained finite Volume(MCV3)scheme.Then it is applied to quasi-uniform cubed-sphere grid,which is designed to avoid the polar problem on the traditional latitude–longitude grid.To suppress the non-physical numerical oscillations,a bound-preserving(BP)algorithm to constrain the conserved advected tracer to within the initial maximum and minimum values is also implemented.The scheme is validated with several widely used benchmarks involving prescribed non-divergent two-dimensional flow on the sphere and different initial tracer distributions.The resulting conservative transport model with high-order accuracy and positive preserving property is comparable to other high-order schemes and has the potential for the numerical simulation of various traces in the atmosphere.
