Application of a Multipurpose Finite Element Solver Condensation Simulation: Use of Adaptive Mesh Refinement and Automatic Time Step Control

摘要

A multipurpose finite element solver for partial differential equation (PDE), which implements adaptive mesh refinement and automatic time step control, is used for solving condensation equation. Instead of empirically determining the mesh and time-step sizes, the sophisticated PDE solver automatically determines the optimum values in the simulation of the condensational growth. The adaptive diffusion coefficient, which depends on the size distribution, stabilizes the calculation without numerically diffusing the shape of the size distribution. The adaptive mesh refinement and automatic time step control realize the accurate calculation of the size distribution and the conservation of the total particle number. Even when the simulated distribution becomes extremely sharp, it gives a result close to the analytical solution. The numerical solutions are accurate enough to be used as the exact ones, which cannot be solved analytically under realistic condition. Since some multipurpose solvers for PDE have been available in scientific modeling and engineering education, these sophisticated and easy-to-use solvers are expected to be actively used in aerosol modeling and education.