The script solves stationary advection-diffusion equation with cylindrical symmetry in polar coordinates for a range of Peclet numbers. Using the found soluion we integrate the flux along the surface of a center particle and find the dependence of aggregation kernel on Peclet number. To speed up computations we use joblib. The equation is solved using an implicit scheme, to solve the sparse linear system we use scipy.sparse. The program doesn't require any command line arguments.
Based on this publication.
- The equation in the proposed problem set can be solved analytically. However due to that fact that the solution is formed by an infinite series, derivation of a simple formula for aggregation kernel is problematic. That is why we use Pade approximation technique. Example of a numerical solution for distinct Peclet numbers:
