The current implementation of the Population Balance Model utilizes a upwind scheme in a Eulerian framework. One of the potential drawbacks of this scheme is a "diffusive"-like behavior at the ends of the particle size distribution (where the distribution will appear discontinuous). Higher order schemes can fix this issue.
One such example is from H. Xiong, Y. Feng, Y. Zhao and H. Zheng, J. of Materi Eng and Perform (2024). https://doi.org/10.1007/s11665-024-09832-6. This adds an amplitude limiter that depends on the change in gradient in the PSD, thereby, limiting fluxes at discontinuous regions (eq 30-34). In practice, while the results of the upwind and higher order schemes are very similar, the upwind scheme can result in a very large upper tail, which can affect performance, where we would have to account for an extra number of bins with near 0 particle density.
The current implementation of the Population Balance Model utilizes a upwind scheme in a Eulerian framework. One of the potential drawbacks of this scheme is a "diffusive"-like behavior at the ends of the particle size distribution (where the distribution will appear discontinuous). Higher order schemes can fix this issue.
One such example is from H. Xiong, Y. Feng, Y. Zhao and H. Zheng, J. of Materi Eng and Perform (2024). https://doi.org/10.1007/s11665-024-09832-6. This adds an amplitude limiter that depends on the change in gradient in the PSD, thereby, limiting fluxes at discontinuous regions (eq 30-34). In practice, while the results of the upwind and higher order schemes are very similar, the upwind scheme can result in a very large upper tail, which can affect performance, where we would have to account for an extra number of bins with near 0 particle density.