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

4. 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. INITIAL MPDATA GAGE UPWIND LEAPFROG

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. AGARD MPDATA + FCT M = 0.8 α = 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. Remeshing Mesh movement Mesh enrichment P-refinement Combinations MESHING TECHNIQUES

29. M = 2.5 α = 0

30. M = 2.5 Cp theoretical = 0.329 Cp computed

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 α m = 1.01deg c=0.5m

34. Mesh movement

35. RAE 2822 M = 0.75 α = 3

36. MPDATA 7523 points AGARD 20580 points

37. MPDATA fine mesh 16101 points enrichment 11915 points

38. M = 0.8 α = 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