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 ( )
ASGS_0s.jpg
ASGS_0sbott.jpg
ASGS_1000s.jpg
ASGS_1000sbott.jpg
ASGS_2000s.jpg
ASGS_2000sbott.jpg








Transport of a passive tracer with a given velocity field:

  • 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")
skamarockRef2.jpg

ASGS_2point5secs_revolution_vsReference0000.jpg
(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


skamarockRef.jpg
ASGS_5secs_revolution_vsReference0000.jpg
(ALYA) ASGS stable. After 5T, back-revolution to initial state
OSS_5secs_revolution_vsReference0000.jpg
(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:

sigmaVSref5000s.jpg
Sigma superimposed with the ref., 5000s


hybridVSref5000s.jpg
Hybrid superimposed with the ref., 5000s

hybridVSref5000s.jpg
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
notopo_vs_schar_t0s0001.jpg
Error at initial state



notopo_vs_schar_t5ks0000.jpg
Error at 5000 s

notopo_vs_schar_t10ks0000.jpg
Error at 10000 s



  • Case 2: Transport on SIGMA grid vs reference state

notopo_vs_sigma_t0s0000.jpg
Initial state on sigma grid


notopo_vs_sigma_t5ks0000.jpg
At 5000 s on SIGMA grid


notopo_vs_sigma_t10ks0001.jpg
At 10000 s on SIGMA grid