Transport


 * Testing the transport abilities of our FEM code through benchmarks:**


 * 2D advection of smooth cone in a rotating velocity field. As defined by different authors
 * [[image:ASGS_0s.jpg width="526" height="482"]] || [[image:ASGS_0sbott.jpg width="467" height="428"]] ||
 * [[image:ASGS_1000s.jpg width="526" height="483"]] || [[image:ASGS_1000sbott.jpg width="503" height="464"]] ||
 * [[image:ASGS_2000s.jpg width="508" height="469"]] || [[image:ASGS_2000sbott.jpg width="505" height="467"]] ||

Transport of a passive tracer with a given velocity field:
 * Case 1) after Durran, 1999: "//[|//Numerical Methods for Wave Equations in Geophysical Fluid Dynamics//]"//


 * Initial state (top) and after 2.5 T (bottom. T is a non-dimensional time). (Top two images taken from Skamarock 2006: "Positive-definiti and monotonic limiters for unrestricted-time-step transport")
 * [[image:skamarockRef2.jpg width="292" height="623" align="center"]]

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 * At 2.5T the flow is reversed and the tracer is expected to return to its initial state at 5T: results presented for different algorithms.
 * Top 4 image taken from Skamarock (2006).
 * Bottom images (red and black) are obtained with the ASGS and OSS stable FEM algorithm developed in ALYA


 * [[image:skamarockRef.jpg]] ||
 * [[image:ASGS_5secs_revolution_vsReference0000.jpg width="793" height="618" caption="(ALYA) ASGS stable. After 5T, back-revolution to initial state"]][[image:OSS_5secs_revolution_vsReference0000.jpg width="815" height="636" align="left" caption="(ALYA) OSS stable. After 5T, back-revolution to initial state"]] ||


 * **Schar transport test (Schar et al. 2002):**


 * The images below represent the tracer distribution computed on a Sigma (top), hybrid (middle) and SLEVE (bottom) vertical grid built around a Schar mountain, and superimposed with the reference distribution obtained without topography:


 * [[image:sigmaVSref5000s.jpg width="697" height="405" caption="Sigma superimposed with the ref., 5000s"]]

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 * __**Error: algebraic difference between the values of different results after interpolation on the reference grid:**__


 * Case 1: Transport on SLEVE grid vs reference state




 * Case 2: Transport on SIGMA grid vs reference state