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Numerical Error Analysis of Solvers Using Cumulative Number Distribution with Volume-Ratio Grid Spacing in Initially Particle-Free Nucleation-Condensation Systems

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Volume: 12 | Issue: 6 | Pages: 1125-1134
DOI: 10.4209/aaqr.2012.02.0042
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Masaru Yamamoto

  • Research Institute for Applied Mechanics, Kyushu University, 6-1 Kasuga-kouen, Kasuga 816-8580, Japan


The numerical accuracy of solvers has not been fully investigated in initially particle-free nucleation-condensation systems, which are important in modeling particle generation in the free-molecular regime. The numerical error analysis of several schemes using the cumulative number function is conducted on the basis of Williams’ analytical solution and the Courant–Friedrich–Lewy (CFL) condition in volume-ratio grid spacing of the particle size. In this system, because the CFL number (obtained from the particle growth rate, grid size, and time step size) depends strongly on the particle size, we need to check the CFL condition (determining the numerical stability and accuracy) over a whole size range before the simulation. This has not been fully discussed in aerosol modeling. The present study introduces a new unique constant (DCFL) throughout the simulation in the volume-ratio grid spacing. In the sensitivity experiments, we can find the similarities of the simulated size distribution and its numerical error, which are determined by the DCFL. We can thus easily check the CFL condition, and choose an appropriate time step size, to satisfy the required accuracy in the nucleation-condensation module of the program.


Numerical error Nucleation Condensation Semi-Lagrangian solver Cumulative number

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