Lagrangian modeling of particle concentration distribution in indoor environment with different kernel functions and particle search algorithms

This study aims at investigating the simulation error and computational efficiency of indoor particulate matter (PM) concentration estimation for various kernel functions and particle search algorithms of the kernel method. Firstly, five kernel functions (the Gaussian, quadratic, cubic, quartic and quintic kernels) together with five released particle number are applied to establish twenty-five scenarios of indoor concentration estimation. Measured PM concentration profiles in indoor chambers are used to identify the most appropriate kernel function among the above scenarios. The simulated results show that the cubic and quartic kernel functions both give the minimum simulation error and they only need about 40% CPU time of the Gaussian kernel function. Next, two particle search algorithms (the all-pair and linked-list algorithms) with the cubic kernel function are tested for various numbers of the released particles and concentration observation points. The present study demonstrates that the linked-list algorithm provides the same accuracy as the all-pair algorithm for indoor PM concentration estimation. However, for the computational efficiency, the linked-list algorithm is proved to be much better than the widely used all-pair algorithm. The required CPU time of the all-pair algorithm can be 28 times as large as the linked-list algorithm when the number of the concentration observation points is more than O(104).

► The Gaussian, quadratic, cubic, quartic and quintic kernel functions are compared.
► The cubic and quartic kernels are the best accuracy and efficient kernel functions.
► The all-pair and the linked-list search algorithms are compared.
► The linked-list algorithm has better efficiency than the all-pair algorithm.