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")

(ALYA) FEM. ASGS stable

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

(ALYA) ASGS stable. After 5T, back-revolution to initial state

(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:

Sigma superimposed with the ref., 5000s

Hybrid superimposed with the ref., 5000s

SLEVE superimposed with the ref., 5000s

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

Case 1: Transport on SLEVE grid vs reference state

Error at initial state

Error at 5000 s

Error at 10000 s

Case 2: Transport on SIGMA grid vs reference state

Testing the transport abilities of our FEM code through benchmarks:Transport of a passive tracer with a given velocity field:

//Numerical Methods for Wave Equations in Geophysical Fluid Dynamics//"Schar transport test (Schar et al. 2002):Error: algebraic difference between the values of different results after interpolation on the reference grid: