1 / 34

On forward in time differencing: an unstructured mesh framework

On forward in time differencing: an unstructured mesh framework. Joanna Szmelter Piotr Smolarkiewicz Loughborough University NCAR UK Colorado USA.

john-curtis
Download Presentation

On forward in time differencing: an unstructured mesh framework

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. On forward in time differencing: anunstructured mesh framework Joanna Szmelter Piotr SmolarkiewiczLoughborough University NCARUK Colorado USA

  2. Edge based dataFinite Volume (Smolarkiewicz, Szmelter JCP 2005) 2D 3D

  3. Edge based data structure ☺Flexiblemesh adaptivity and hybrid meshes☺Low storage☺Easy generalisation to 3D, vectorisation, parallelisation, mesh agglomeration☺ Less expensive than element based data structure More expensive operations than I,J,K

  4. Notion of the edge-based MPDATA: ADVECTION FIRST ORDER UPWIND (DONOR CELL) compensating velocity

  5. MPDATA BASIC SCHEME ITERATED UPWIND FIRST ORDER UPWIND FIRST ORDER UPWIND

  6. Structured v Unstructured

  7. CONVERGENCE OF FINITE-VOLUME MPDATA ON UNSTRUCTURED MESH

  8. CONVERGENCE OF FINITE-VOLUME MPDATA ON UNSTRUCTURED SKEWED MESH

  9. REVOLUTION OF A SPHERE AROUND THE DIAGONAL OF A DOMAIN MPDATA GAGE AFTER 1 REVOLUTION INITIAL

  10. NFT MPDATA: a general template implicit integration preconditioned non-symmetric Krylov-subspace elliptic solver explicit integration

  11. Compressible flows Explicit integration (Smolarkiewicz, Szmelter JCP 2008 published on line)

  12. Internal Energy Equation • Potential Temperature Equation Classical Total Energy Equation • Modified Total Energy Equation

  13. Supersonic flows Mesh adaptivity by remeshing M = 5 M =2. 5 M = 15

  14. ADAPTIVITY with a refinement indicator based on MPDATA lead error (Szmelter,Smolarkiewicz IJNMF 2005) Mesh movement Point enrichment

  15. NACA012 M=0.85 α=1.25º Transonic flow MPDATA Runge-Kutta

  16. CONVERGENCE STUDY MPDATA - NFT EULER SOLVER M=0.5 MPDATA UPWIND

  17. Flow past a cylinder M=0.38

  18. Flow past a cylinder M=0.38 --- Entropy deviation triangular meshes Internal energy Total energy Potential temperature Modified total energy

  19. M=0 3D Spherical wave; Analytical solution --- Landau & Lifshitz

  20. Incompressible flows Implicit integration

  21. Incompressible flows Re=200. Strouhal number =183 Re=100. Strouhal number =163

  22. Incompressible flows --- multi-connected domains Re=100

  23. 2D – non-hydrostatic model IncompressibleBoussinesq ILES Orographically forced atmospheric gravity waves vertical wave propagation wave breaking

  24. Flows on a Sphere --- Geospherical coordinates

  25. Shallow water equations initial

  26. Shallow water equations

  27. Shallow water equations Zonal flow over a cone

  28. Potential for modelling of multi-connected domains and easy implementation of mesh adaptivity. (David Parkinson) (Treatment of hanging nodes & hybrid meshes Szmelter et al Comp. Meth. Appl. Mech. Eng 92)

  29. IMPORTANCE OF SCHEME’S MULTIDIMENSIONALITY Remapping for ALE---Prescribed tensor product grid movement Oblique Shock (Ryan Hill) MPDATA van Leer

  30. Remapping for ALE---Prescribed tensor product grid movement • Smooth saddle distribution MPDATA van Leer

  31. CONCLUSIONS • Presented work opens avenues to construct a flexible edge-based clone of EULAG and to study unstructured meshes performance for all-scale atmospheric flows. • Main new effort lies in mesh generation, visualisation and parallelisation.

  32. CFD and mesh generation

  33. Advection on a Sphere

More Related