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Published byLaureen Marshall Modified over 9 years ago
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2/11/2010 1 Research Review
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Geodesic Grids Finite volume transport Reconstruction functions Mass Flux Calculations Monotonic Limiting 2/11/2010 2 Research Review
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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
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Transport Equation Integrating over the area Integrating in time gives 2/11/2010 4 Research Review
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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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Various Cases 2/11/2010 7 Research Review
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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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Area- Avg -Quad Area Cubic e^(x) 2/11/2010 14 Research Review
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SOLUTION : MONOTONICITY CONSTRAINT 2/11/2010 15 Research Review
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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
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M D T Z 2/11/2010 17 Research Review
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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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