High-order polynomial approximations for solving non-inertial particle size density in flames

A novel numerical framework is discussed to simulate the time evolution of non-inertial particle size distributions (or number density functions) in flames. The generic form population balance equation considered featuring nucleation, surface growth/loss and agglomeration/coagulation. This first recast a that prone minimize spurious errors simulation collision integrals. Formally, this achieved classifying terms into: (i) Lagrangian transport size-space (surface growth/loss), (ii) relaxation rates at given (non-uniform negative contribution integrals) (iii) sources (nucleation positive integrals). To secure accuracy, high-order modal decomposition distribution introduced within every section considered. Legendre polynomials basis used with Gauss-Lobatto quadrature points. By construction, method performs very well for dealing it also highly accurate estimation integrals thanks quadrature. confirmed simulating canonical test cases literature compare results against exact analytical solutions. With discretisation based on about 40 sections interpolation 5th-order, good accuracy obtained up third moment ranging over 8 orders magnitude. cast computing cost. Strategies couple carbon particles dynamics flames are discussed.