1 / 16

Application of the CSLR on the “Yin-Yang” Grid in Spherical Geometry

Application of the CSLR on the “Yin-Yang” Grid in Spherical Geometry. X. Peng (Earth Simulator Center) F. Xiao (Tokyo Institute of Technology) K. Takahashi (Earth Simulator Center). PDE2004-15:10-15:30 July20,2004, Yokohama. Present requirements and Issues.

ward
Download Presentation

Application of the CSLR on the “Yin-Yang” Grid in Spherical Geometry

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Application of the CSLR on the “Yin-Yang” Grid in Spherical Geometry X. Peng (Earth Simulator Center) F. Xiao (Tokyo Institute of Technology) K. Takahashi (Earth Simulator Center) PDE2004-15:10-15:30 July20,2004, Yokohama

  2. Present requirements and Issues • Model development (global, non-hydrostatic, high-resolution) on sphere • Requirement of high-accuracy, high-efficiency and high-performance computation to save CPU time. Problems in global high-resolution model • Singularity of ordinary latitude-longitude coordinate • Solid Courant number limitation • “Negative mass” and non-conservative advection A possible solution:using positive-definite, conservative semi-Lagrangian scheme on quasi-uniform grid without singular point.

  3. CIP-CSLR • Conservative semi-Lagrangian scheme with rational function (Xiao et al. 2002) based CIP (Constrained Interpolation Profile, Yabe et al. 1991) • Predicts both the cell-integrated and interface values, which makes it more accurate but increase little computation. • Be conservative, oscillation-free, positive-definite but no additional limiter needed. • A high-accuracy scheme over merely one cell.

  4. CIP algorithm 1D advection Differentiate (1) in x direction, we get Here, (1) and (2) are advection equation in the same formation, the only difference is the forcing term (RHT). (1) (2)

  5. CIP-CSLR algorithm Refer to Xiao et al. 2002, JGR,107(D22),4609 1D advection (flux-form) is Suppose We have Using the same stencil, we construct conservative scheme. Also the rational function make the scheme be positive, monotonic  convexity preserving (3) (4)

  6. ☯ Yin-Yang grid 【Yi Jing: the Book of Changes】 The universe（both space and time） can be divided into Yin and Yang, Which is composed with metals(金), water(水), wood(木), fire(火) and soil(土). For example, the moon is Yin, and the sun is Yang. The energy of the atmosphere comes from the sun. Yang (N) zone Yin (E) zone Yin-Yang composition ＋ ＝ Provided by Dr. Kageyama, ESC, who proposed the Yin-Yang grid

  7. Yin-Yang grid structure In the Mercator projection

  8. Some features of Yin-Yang grid • Overset grid • Orthogonal coordinates（same as the lat-lon geometry） • No polar singularity-- high computational efficiency. • The same grid structure of Yin and Yang components. • Easy to nest • Easy to parallelize (with domain selecting) • But need to take care of conservation law.

  9. The application to latitude-longitude or Yin-Yang grid system Dynamical equation in spherical geometry Modified to fully-flux form in For Yin-Yang grid system, the same equation is used for both Yin and Yang zones.

  10. Solid advection in Yin-Yang grid (np=40,CFL=1) dlat=dlon=2.25° • Wilianmson et al. (1992) test case 1. • Linear interpolation for Yin&Yang boundary. • Initial condition is distributed to lat-lon grid first, then interpolate to Yin, Yang zone. • Yin, Yang is plotted separately. YANG YANG YIN YIN Meridional advection Zonal advection

  11. Results （２）　 np=40 CFL=３ dlat=dlon=2.25° • Wilianmson et al. (1992) test 1 • Linear interpolation to Yin,Yang’s boundary • CFL=3 YANG YANG YIN YIN Zonal advection Meridional advection

  12. Global mass variation dlat=dlon=1.125° α=0.0 α=π/2

  13. The conservative scheme The necessary and sufficient condition for global conservation is as Yin The sufficient condition is Yang dΓ denotes any part of the boundary of N,E, e.g. EF.

  14. Solid advection test np=80,CFL=1 α=0.0 α=π/2

  15. Solid advection test With large Courant number np=80

  16. Summary • Precise advection is achieved with the CIP-CSLR that is positive-definite, shape-preserving. • High-efficient computation is also successful using CIP-CSLR on the Yin-Yang grid. The minimum and maximum grid intervals in the Yin-Yang system bears a proportion of 0.707. Much longer time step is available under the same Courant number, in comparing with ordinary Lat-Lon grid. It is 144 times larger at the resolution of 0.5625 degree. • Being orthogonal grid, it is easy to implement time splitting procedure • Accuracy in polar region is greatly improved. • Large Courant number is available, which is a possible in high resolution model. • Global conservation is developed, and is confirmed with the idealized advection.

More Related