Dear mailinglist, I am trying to solve a convection problem where the convected substance is adsorbed (on active carbon in this case). It is modeled as follows: the fluid is divided in a bulk part and in a film layer part; that is the film layer surrounding the adsorbing medium (active carbon). To the concentration in the bulk applies a convective equation with a sink for the part of the solute that is diffusing into the film layer; the sink depends on the difference between film and bulk concentration. The film layer thus receives the solute from the bulk and loses it to the adsorbing medium and is therefore modeled as an equation with only a sink and a source; the source depends on the concentration difference between bulk and film, the sink depends on the 'concentration' difference between the surface and the center of active carbon grains. Finally, I also modeled the diffusion of the solute from the surface of the active carbon to its center; this source term depends on the difference between solution at the surface and center of the grain.
c_b: bulk concentration c_f: film concentration q_s: concentration at the surface of the grain (this is not really a concentration, but the amount of adsorbed material per amount of adsorbing material (active carbon) q_b: the concentration in the center of the grain This then yields the following equations: dc_b/dt = v dc_b/dx - A1(c_b - c_f) dc_f/dt = A2 (c_b - c_f) - A3(q_s - q_b) dq_s/dt = A4(q_s - q_b) here A1, A2, A3 and A4 are some mass transfer constants. Furthermore, q_s relates to c_f by the Freundlich equation: q_s = K_Fr * c_f ^n_Fr where K_Fr and n_Fr are the (Freundlich) constants. Implementation is attached as minimal working example. My problem is that this only converges at very small timesteps, that is of order of seconds, while I need to simulate order of years. I need larger timesteps, but I do not know how to improve this further. The changes in time are not so large, so it should be possible. Apparently this is some tricky numerical issue. I tried all the different solvers in FiPy and it seemed that the most stable solution occurs using LinearLUSolver with zero gradient outlet boundary condition at the outlet. I linearized the non-linear isotherm which increased my allowed timestep from milliseconds to seconds. Can you help me improve my simulation speed? I hope you have sufficient information with the implementation and value of the constants as attached and given below. If not, please let me know. Value for the constants: A1 = 0.36 A2 = 0.48 A3 = 0.0148 A4 = 1.e-8 v = 1.6e-3 # m/s K_Fr = 386 N_Fr = 0.33 Best regards, M.W. (Martin) Korevaar, MSc Scientific researcher - Drinking Water Treatment | KWR Watercycle Research Institute | Groningenhaven 7, P.O. Box 1072, 3430 BB Nieuwegein, the Netherlands [http://www.kwrwater.nl/uploadedImages/mail/gmaps.png] <https://maps.google.nl/maps?q=Groningenhaven+7,+3433+PE+Nieuwegein&hl=nl&sll=52.212992,5.27937&sspn=4.678847,13.392334&t=m&hnear=Groningenhaven+7,+3433+PE+Nieuwegein,+Utrecht&z=16> | T +31 30 606 9515 | M +31 6 11648156 | E martin.korev...@kwrwater.nl<mailto:martin.korev...@kwrwater.nl> | W www.kwrwater.nl<http://www.kwrwater.nl> | Follow KWR on [http://www.kwrwater.nl/uploadedImages/mail/twitter.png] <http://www.twitter.com/kwr_water> | Follow me on [http://www.kwrwater.nl/uploadedImages/mail/linkedin.png] <https://nl.linkedin.com/in/martinkorevaar> | Chamber of Commerce Utrecht e.o. 27279653. The KWR office building<http://www.kwrwater.nl/BNA_Gebouw_van_het_Jaar/> has won the 'Most Stimulating Environment' award of the Royal Institute of Dutch Architects.
MWE.py
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