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Error Indicator based on the Multidimensional Positive Definite Advection Transport Algorithm (MPDATA)

Error Indicator based on the Multidimensional Positive Definite Advection Transport Algorithm (MPDATA). Joanna Szmelter Piotr K. Smolarkiewicz Cranfield University NCAR Royal Military College of Science Boulder

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Error Indicator based on the Multidimensional Positive Definite Advection Transport Algorithm (MPDATA)

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  1. Error Indicator based on the Multidimensional Positive Definite Advection Transport Algorithm (MPDATA) Joanna Szmelter Piotr K. Smolarkiewicz Cranfield University NCAR Royal Military College of Science Boulder Shrivenham Colorado

  2. Cartesian mesh MPDATA

  3. Cartesian mesh MPDATA

  4. MPDATA BASIC SCHEME

  5. MPDATA BASIC SCHEME

  6. MPDATA BASIC SCHEME

  7. EDGE BASED FORMULATION

  8. CONVERGENCE OF FINITE-VOLUME MPDATA ON UNSTRUCTURED MESH

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

  10. ROTATING CYLINDER BASIC MPDATA MPDATA+FTC

  11. FCT

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

  13. MPDATA GAGE INITIAL LEAPFROG UPWIND

  14. EULER EQUATIONS – CONSERVATIVE FORM

  15. NONOSCILLATORY FORWARD IN TIME FLOW SOLVERS

  16. FLOW SOLVER

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

  18. NACA 0012 COMPUTATIONAL MESH

  19. MPDATA + FCT AGARD M = 0.8α= 1.25

  20. MPDATA v AGARD SOLUTION

  21. THE SAME MESH MPDATA v R-K SOLUTION

  22. EFFECT OF FCT

  23. EFFECT OF PRESSURE SWITCH

  24. ADAPTIVITY • REFINEMENT INDICATORS • MESHING TECHNIQUES

  25. REFINEMENT INDICATORS • From gradient of dependent variable • Based on MPDATA lead error • In the spirit of Richardson extrapolation • Driven by an objective functional

  26. LEAD ERROR

  27. MPDATA ERROR INDICATOR

  28. MESHING TECHNIQUES • Remeshing • Mesh movement • Mesh enrichment • P-refinement • Combinations

  29. M = 2.5 α= 0

  30. M = 2.5 Cp theoretical = 0.329 Cp computed <0.3334,0.3339>

  31. M = 5 M = 15

  32. Comparison of theoretical and computed shock angles for 15deg wedge

  33. NACA64A010 OSCILLATING AEROFOIL M=0.796 k=0.2002 αm =1.01deg c=0.5m

  34. Mesh movement

  35. RAE 2822 M = 0.75α= 3

  36. RAE 2822 M = 0.75α= 3 MPDATA 7523 points AGARD 20580 points

  37. MPDATA fine mesh 16101 points enrichment 11915 points

  38. M = 0.8α= 1.25 Pressure Contours

  39. CONCLUSIONS • MPDATA evinces properties useful for construction of refinement indicators. • Edge-based data structure enables the use of MPDATA in conjunction with all standard adaptive meshing techniques known for unstructured meshes. • NFT MPDATA edge-based Euler solver has low implicit diffusion and remains accurate for a broad range of flow speeds. • Present work extends utility of MPDATA to new applications

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