Trying to reproduce an advection diffusion problem


I am trying to reproduce the test results of the paper “an innovative LB model for simulating Michaelis-Menten-based diffusion-advection kinetics and its application within a cartilage cell bioreactor” from Moaty et. al.

The fact is that I have problems to reach to a peak of 0.16 after 1.25s in the exposed model at fig 6-7.

I am not sure what is happening, but when I set my diffusivity very low, I get instabilities of negative concentration values near in the coordinates near the pulse at C_0 = 1. This happends because a very low diffusivity is traduced to a very narrow concentration relaxation time to 0.5.

The fact is that I think that my dimensional analysis is correct. But I am not very sure how the paper implements Diffusivity, D = 0.01 in lattice or real units. what is for sure is that if I set it at 0.01, the concentration values at the center of the concentration pulse after 1.25s is 0.03, which is far lower from the 0.16 reference value. However, if I lower the diffusivity I get these concentration instabilities…

I had already solved the problem, it seems that in the formula to initialize the concentration with a pulse was lacking a time factor to make it consistent…