1 / 32

Jia-Fong Fan and Hann-Ming Henry Juang Environmental M odeling C enter NCEP/NWS/NOAA

Applied Non-iteration Dimensional-split Semi- Lagrangian Advection with Riemann Invariant Characteristic Equation in Non-hydrostatic System. Jia-Fong Fan and Hann-Ming Henry Juang Environmental M odeling C enter NCEP/NWS/NOAA. 11th RSM workshop, NCU, Taiwan. Introduction.

dewey
Download Presentation

Jia-Fong Fan and Hann-Ming Henry Juang Environmental M odeling C enter NCEP/NWS/NOAA

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. AppliedNon-iteration Dimensional-split Semi-Lagrangian Advectionwith Riemann Invariant Characteristic Equation in Non-hydrostatic System Jia-Fong Fan and Hann-Ming Henry Juang EnvironmentalModelingCenter NCEP/NWS/NOAA 11th RSM workshop, NCU, Taiwan

  2. Introduction • Primitive equations without approximation contains high- frequency sound waves. These waves impose a severe restriction on the size of time step in order to produce stable integrations. The most common practice consists of using approximations that eliminate sound waves from the equations. Large-scale models use the hydrostatic approximation. Convection models generally use the anelastic approximation. • Inthisstudy,wecombinenon-iterationdimensional-splitsemi-Largrangian(NDSL)advectionwithRiemanninvariantcharacteristic equation (RICE)tosolveacousticwaveexplicitly.WetestNDSL-RICEmethodinanon-hydrostaticsystem.

  3. Non-hydrostatic equation on xz can be written as

  4. 1D test For Riemann solver, we let the above equations be where

  5. Initial condition and after 400s

  6. The initial acoustic spread

  7. After 800s with different CFL

  8. 2D tests in x-z withisotherm where

  9. 2D tests in x-y (non-forcing) • Here,setg=0,itmeansonax-yplane,andweignoreallforcingtermtomakesureRiemannsolverperformwellin2Dspatialsplitting. • ForRiemannsolver,wewriteitinto Xdirection: Zdirection:

  10. 2D tests in x-y (non-forcing) Experimentsetting Initial Condition: Domain:

  11. 2D tests in x-y (non-forcing) – Q’(t=30s)

  12. 2D tests in x-y (non-forcing) – Q’(t=60s)

  13. 2D tests in x-y (non-forcing) – Q’(t=120s)

  14. 2D tests in x-y (non-forcing) – U(t=30s)

  15. 2D tests in x-y (non-forcing) – U(t=60s)

  16. 2D tests in x-y (non-forcing) – U(t=120s)

  17. 2D tests in x-y (non-forcing) – V(t=30s)

  18. 2D tests in x-y (non-forcing) – V(t=60s)

  19. 2D tests in x-y (non-forcing) – V(t=120s)

  20. Warm bubblecase • Non-hydrostaticequationonxzcanbewrittenas

  21. Warmbubblecase • ForRiemannsolver,wewriteitinto

  22. Warmbubblecase- sequential forcing Forxdirection Forzdirection:

  23. Warm Bubble case Initial Condition: Experimentsetting Bubble center(51,27) Domain:

  24. WarmBubbleCase Time-step=0.01s, CFL~0.7

  25. Results Comparison with lecture by Andre Robert 1992

  26. Warmbubblecase U speed time step=0.01 CFL~0.7

  27. W speedtime step=0.01 CFL~0.7

  28. Cascade interpolation

  29. Conclusion • A non-hydrostatic equation system is used to test NDSL-RICE method to resolve acoustic waves explicitly. Since NDSL is unconditionally stable for advection, theoretically we can use as large a time step as possible; however, RICE in two-dimensions shows ill-solution with large time step. • Thus, the preliminary results show that no limitation of time step should be used in one-dimensional tests but there are some limitations in two dimensional tests due to the nature of Riemann solver. Furthermore, the long distance advection due to large acoustic speeds require us to consider entire trajectory as compared to central mean value.

  30. Future work • Applied cascade interpolation with NDSL-RICE on warm bubble test • Improve processes for forcing term

  31. -ThankYou-

More Related