/Parallel_Coagulation_Kernel

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Parallelization Scheme for Modeling Coagulation

Team Members

  • Ziyu Huang
  • Kevin Sampson

The "Big" Problem

  • Modeling the time evolution of number densities of particles experiencing coagulation (or clumping together) is extremely computationally intensive

  • Often takes up to several days to process on a cluster like USC CARC!

  • Most famous and relevant equation for describing this evolution of coagulating particles is the Smoluchowski Coagulation Equation:

$$\frac{d}{d t} f_k=\frac{1}{2} \sum_{i+j=k} K(i, j) f_i f_j-\sum_i K(i, k) f_i f_k$$

  • $K$ is the coefficient for coagulation between i and j (sticking coefficient)
  • $f_k$ is the number density of particle with mass $m = k$.

Importance

  • Equation is also crucial for atmospheric particles, aerosols and — most importantly — interstellar dust.
  • Since no parallelized version for integrated models for this solver exist, this step has become a bottleneck in the modeling process for coagulation.

Proposed Solution

  • PARALLELIZE the numerical solver for the Smoluchowski coagulation equation.

Applications

  • Interstellar Dust Coagulation

Sequential test case: K = 1

K = 1

$N(m, t)=\frac{N_0}{m_0}\left(\frac{2}{N_0 t}\right)^2 \exp \left[\frac{2}{N_0 t}\left(1-\frac{m}{m_0}\right)\right]$

Work To Do