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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.

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On forward in time differencing: an unstructured mesh framework

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  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

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