Table Of Contents

This Page

05.17.2014: Behavior-of-P-V-system-with-difusion-and-advection

Here is the list of experiments performed recently:

  • patch_virus_1: 64x64 points, dt=0.025, Ps=1 everywhere, V=0.1 inside a patch, no diffusion, no advection, no zooplankton (Figs. 1a, b and c)
  • patch_virus_6: 100x100 points, dt=0.025, Ps=1 everywhere, V=0.1 inside a patch, diffusion diffk=0.1, no advection, no zooplankton (Fig. 2)
  • patch_virus_4: 100x100 points, dt=0.025, Ps=1 everywhere, V=0.1 inside a patch, diffusion diffk=19., no advection, no zooplankton (Fig. 3)
  • patch_virus_7: 100x100 points, dt=0.025, Ps=1 everywhere, V=0.1 inside a patch, diffusion diffk=38., no advection, no zooplankton (Fig. 4)
  • patch_virus_8: 256x256 points, dt=0.0125, Ps=1 everywhere, V=0.1 inside a patch, diffusion diffk=38., no advection, no zooplankton (Fig. 5)
  • patch_virus_9: 256x256 points, dt=0.0125, Ps=1 everywhere, V=0.1 inside a patch, diffusion diffk=100., no advection, no zooplankton (Fig. 6)
  • patch_virus_10: 256x256 points, dt=0.0125, Ps=1 everywhere, V=0.1 inside a patch, diffusion diffk=0.1., no advection, no zooplankton (Fig. 7)
  • patch_virus_11: 256x256 points, dt=0.0125, Ps=1 everywhere, V=0.1 inside a patch, diffusion diffk=0.1, no zooplankton but chaotic advection (Figs. 8a and b)
  • patch_virus_12: 256x256 points, dt=0.0125, Ps=1 everywhere, V=0.1 inside a patch, diffusion diffk=0.01, no zooplankton but chaotic advection
  • patch_virus_13: 256x256 points, dt=0.0125, Ps=1 everywhere, V=0.1 inside a patch, diffusion diffk=1.0, no zooplankton but chaotic advection.
  • patch_virus_14: 256x256 points, dt=0.0125, Ps=1 everywhere, V=0.1 inside a patch, diffusion diffk=10, no zooplankton but chaotic advection.

We start with a low resolution (64x64 points) simulation with no diffusion and advection (patch_virus_1). The initial conditions are Ps=1 everywhere and there is a patch of virus V=0.1 in the center of the domain. The system oscillates until it reaches an equilibrium with Ps=1 outside the patch and equilivrated values of Ps and V inside the patch (Figs. 1a, b and c).

We then increase the diffusion (diffk``=0.1, 19 and 38) with a simulation with 128x128 points (``patch_virus_6, patch_virus_4, patch_virus_7): the front of the inside patch propagates outward, with the speed increasing with the diffusivity coefficient, but not proportionally (Figs. 2, 3 and 4).

Using 256x256 points and diffk``=38 (``patch_virus_8), we find that the front propagates slower than with 128x128 points (patch_virus_7) (Fig. 5). Why? The diffusion in the present case acts at the grid scale. With 256x256 points, the gradient would be sharper and that should correspond to a lower-resolution case with higher diffusivity coefficient and thus faster front. What is wrong with this reasoning?

We then increase the diffusion, diffk=100 (patch_virus_9) or decrease it, diffk=0.1 (patch_virus_10) with the same resolution. The front does not propagate faster in the former case but it does propagate slower in the latter case. Using 100x100 points, I have also noticed that after some threshold value for the diffusivity coefficient, the front does not propagate faster. I did not find any reason why the code would produce such threshold so I still do not understand why this is happening.

We then introduce chaotic advection (coef=0.7*Lbox) for different values of diffk (0.1, 0.01, 1 and 10 for patch_virus_11, patch_virus_12, patch_virus_13 and patch_virus_14, respectively). The spatially-averaged Ps for these simulations is plotted in Fig. 9. There is no change and I do not understand why. If we take the simple example of a one-dimensional front, the stronger the diffusivity, the faster the front should flatten, is not it?). Maybe, this is indicative that all of the diffusion that is occurring is numerical diffusion and we would need a much stronger diffusion to see an effect of the explicit diffusion.

patch_virus_1

../../../../../../_images/snapshots_1.png

Figure 1a: Snapshots in patch_virus_1.

../../../../../../_images/timeseries_1.png

Figure 1b: Time series of spatially averaged quantity in patch_virus_1.

../../../../../../_images/yt_section_1.png

Figure 1b: Time series along x=50 km in patch_virus_1.

patch_virus_6

../../../../../../_images/yt_section_6.png

Figure 2: Time series along x=50 km in patch_virus_6.

patch_virus_4

../../../../../../_images/yt_section_4.png

Figure 3: Time series along x=50 km in patch_virus_4.

patch_virus_7

../../../../../../_images/yt_section_7.png

Figure 4: Time series along x=50 km in patch_virus_7.

patch_virus_8

../../../../../../_images/yt_section_8.png

Figure 5: Time series along x=50 km in patch_virus_8.

patch_virus_9

../../../../../../_images/yt_section_9.png

Figure 6: Time series along x=50 km in patch_virus_9.

patch_virus_10

../../../../../../_images/yt_section_10.png

Figure 7: Time series along x=50 km in patch_virus_10.

patch_virus_11

../../../../../../_images/yt_section_11.png

Figure 8a: Time series along x=50 km in patch_virus_11.

../../../../../../_images/snapshots_11.png

Figure 8b: Time series along x=50 km in patch_virus_11.

patch_virus_11, patch_virus_12, patch_virus_13 and patch_virus_14

../../../../../../_images/diag_num_diff_2_11_12_13_14.png

Figure 9: Spatially-averaged Ps in patch_virus_11, patch_virus_12, patch_virus_13 and patch_virus_14.

Note from meeting with Kelvin (05/20/2014)

  • Look at characteristics of a Fisher’s wave. Does it match what I see in the numerical simulations?

Snapshots and histograms are plotted with plot_snapshot_current_run.py and plot_diag_num_diff_3.py in RESEARCH/MODELISATION/marine_viruses/current_version/runs/run_002/analysis/ on ipu1.