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2.  Geodesic Grids  Finite volume transport  Reconstruction functions  Mass Flux Calculations  Monotonic Limiting 2/11/2010 2 Research Review

3. Source: NCAR Source: Wikipedia  Geodesic grids: Tessellations of the sphere generated from platonic solids  Motivation :To avoid the POLE PROBLEM  Problem: Traditional finite difference methods are not applicable – grid lines not aligned to latitude/longitude 2/11/2010 3 Research Review

4.  Transport Equation  Integrating over the area  Integrating in time gives 2/11/2010 4 Research Review

5. Note : In three cases, Depending on V the q estimate will be different. (Trajectory Calculation) Reconstruction Function Constant Linear Quadratic 2/11/2010 5 Research Review

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7. Various Cases 2/11/2010 7 Research Review

8. Note : In three cases, Depending on V the q estimate will be different. (Trajectory Calculation) Reconstruction Function Constant Linear Quadratic 2/11/2010 8 Research Review

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14. Area- Avg -Quad Area Cubic e^(x) 2/11/2010 14 Research Review

15. SOLUTION : MONOTONICITY CONSTRAINT 2/11/2010 15 Research Review

16. Zalesek Keep as much as weighing of higher order estimate as possible and at the same time preserving the monotonicity. (Details in Zalesek,1979) Vanleer : Gradients are limited for each hexagon as described in Dukowicz and Kodis(1987) Thuburn: A multidimensional flux limiter which modifies the estimated mixing ratio values at the edge itself.( details in Thuburn 1996) 2/11/2010 16 Research Review

17. M D T Z 2/11/2010 17 Research Review

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19.  Geodesic Grids are attractive because are computationally more efficient for AGCM  Steps involved in Tracer transport are a) Compute reconstruction; b) Compute Mass flux; c) Monotonic limiting ( if needed)  Accuracy of reconstruction function determines the convergence order of scheme  Mass flux calculation are important and are responsible for overall computational cost of scheme  Monotonic limiting is important and has been successfully tested 2/11/2010 Research Review 19

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