Fig 1.
The computational domain with different regions.
The top part is the well mixed bulk liquid region, the middle part is the diffusion boundary layer region, and the bottom part represents the biofilm region.
Fig 2.
An example of (partial) input script for NUFEB simulation.
A list of “fix” commands defines IbM processes that apply to the simulation, which includes Monod-based growth (k1), nutrient mass balance (k2), cell division (d1), and EPS production (e1). Each fix command may require one or more parameters for the model specification, such as EPS density (EPSdens), division diameter (divDia), and HET reduction factor in anoxic condition (etaHET). The last parameter is introduced due to the fact that the observed growth rate of HET in anoxic condition was always smaller than that in aerobic condition.
Fig 3.
Block diagram of CFD-DEM coupling.
Diagram adopted from [39]. Fluid dynamics is solved in the CFD module and particle motion is solved in the DEM module. Particle and field information are transferred between the two modules based on an averaging procedure.
Fig 4.
Biofilm deformation and detachment at Uf = 0.2 m s−1.
(a) Time = 0; (b) Time = 0.0015s; (c) Time = 0.003s; (d) Time = 0.01s. The model simulates 4 × 104 particles. Particles crossing the domain boundary will be removed from the system. Particle colours are blue for heterotrophs and grey for EPS. CPU time is 8 hours with dual processors, and initial particle number is 41210.
Fig 5.
Effect of emergent properties on biofilm detachment.
(a) biomasss area density, and (b) biofilm surface roughness.
Fig 6.
Biofilm development after 0, 60, 120, and 160 hours.
The simulation uses 100 processors and 30 hours CPU time to reach 2.3 × 107 particles. The biological timestep is 0.25 hour. Particle colours are blue for heterotrophs, grey for EPS, light blue for AOB, and green for NOB.
Fig 7.
Nitrite concentration field at a small part of the simulated domain after 60 hours.
The spatial distribution of NO2− concentration follows the nitrifier distribution. The areas where NO2− accumulates are due to production by AOB.
Fig 8.
Quantitative evaluation of Case Study 2.
(a) Total biomass of active functional groups over time, and (b) nutrients concentration in bulk liquid. Note that we assume the oxygen concentration in bulk liquid is kept constant by aeration. The slow growth of NOBs is due to the nutrient limitation, their low growth rate, and spatial distribution. At the early stage of the biofilm formation, the system is in NO2− limited condition. As the biofilm growth, the bottom area where NOBs reside turns to oxygen-limited condition. Both conditions inhibit NOBs growth.
Fig 9.
Performance of Case Study 2 with 4–256 processors.
The initial conditions and the model parameters are kept the same in all cases. The average achieved particle number of all cases is 4.77 × 106 with 0.5% standard deviation. The difference is due to the randomness in sub-domains. The simulation with 4 processors is regarded as baseline case for computing speed-up. Doubling the numbers of processors results in almost double speed-up when small processor numbers are employed (e.g., less than 32). However, the speed-up and parallel efficiency decrease with increasing numbers of processors due to inter-processor communication.