Study Of Mass Conservation And Advection Scheme On The Yin-Yang Grid

As one spherical qusi-uniform grid, the Yin-Yang grid is able to avoid the―pole problem‖of the latitude-longitude grid, which is known as the coordinate singularity and the gridconvergence near the poles. However, the global mass non-conservation prevents it fromimmediate application to the atmospheric general circulation models(GCM) and climatesimulation where conservation is essential. In addition, transportation process is one of thebasic dynamical processes in numerical weather prediction(NWP) model, thus high-accuracyadvection scheme has an important impact on the performance of numercial model. Therefore,the advection model on the Yin-Yang grid is studyed with two kind of advection schemeswhich are the conservative Conservative Semi-Lagrangian with Rational function(CSLR)advection scheme and the3rd-order Runge-Kutta time integration method combined with5th-order finite difference advection scheme(hereafer called―RK3-FD5‖). Out of them, themass conservation problem on the Yin-Yang overlap grid is mainly discussed. The presentstudy consists of the following three parts:1、The CSLR advection scheme is investigated. Focusing on the convergence rate, theCSLR is tested under different conditions in the Cartesian plane coordinate and sphericallatitude-longitude coordinate systerm. Numerical results indicat that the CSLR scheme couldacquire monotonicity and positive definition with the1D rational function for1D and2Dcomputations. The convergence rate of the CSLR scheme is about second order and itshigh-accuracy reflects in descibing discontinuity or strong gradient without any other limiter.In the multi-dimensional computation, the splitting method is adopted and preserves thespecial character of the1D rational function, but at the cost of the accuracy and convergencerate being reduced somewhat. The performance of this kind of Semi-Lagrangian method isalso affected by the―pole problem‖and spherical curvature when implemented inlatitude-longitude grid.2、The study of mass conservation method on the Yin-Yang grid. With the intermediatecomputational results of the CSLR scheme and multi-momemt (M-)grid, three massconservation schemes on the overset grid are constructed and related numerical tests are performed for comparison. It is founded that manual mass-variation vanish (MV) method canensure mass conservation effectively and has no obvious effect on the numerical computation.This method is also sutiable for flux-form and advective-form advection equation as well.The sub-grid mass distibution is considered and a piece-wise mass linear distribution(ML)method is built. On one hand, the method improves the computational results compared withthe piece-wise mass constant distribution(MC) method. On the other hand, the ML methodwill increase computational cost because of time-dependent mass reconstruction. Thusconsidering the accuracy and computional cost, the MC method is more suitable for realapplication and may be a effective scheme of ensuring local and global mass conservation.3、Constructing the RK3-FD5finite difference advection model on the Yin-Yang grid. Inorder to improve the accuracy of time integration and flux calculation, the RK3-FD5advection scheme is implemented into the Yin-Yang grid. The advection scheme is firstlyevaluated and then is adopted in the Yin-Yang grid to construct advection model. The resultsreflect that the RK3-FD5advection scheme can obtain at least third order converance rate onthe Cartisian plane system when uniform grid is setted. However, the scheme acquires2nd–3rdorder in the spherical lat-lon grid because of non-uniform finite difference and―poleproblem‖. When the5thorder Lagrangian interpolation method is implemented, the2ndorderadvection results are acquired on the Yin-Yang grid. Furthermore, if the mass conservationlimitation method (MC) is added to the computation, the convergence rate remains to be2nd-order without obviously increasing computational error under the mass conservativecondition.