Proper Orthogonal Decomposition--Lattice Boltzmann Method: Simulating the Air Pollutant Problem in Street Canyon Areas
Reza MohammadiArani, Mehdi Dehghan, Mostafa Abbaszadeh
Abstract
Recently, the reduced order model (ROM) has been applied to reduce the computational cost of numerical methods. Merging this approach with the lattice Boltzmann method (LBM) as a powerful mesoscale fluid solver seems promising. Dealing with this idea requires a matrix form for the LBM. This matrix form must represent all the LBM's algorithm steps (including boundary condition implementation) to just one specific matrix-vector relation. Furthermore, the LBM contains some nonlinear parts inside the equilibrium distribution function (EDF), which must be treated with a nonlinear ROM like the discrete empirical interpolation method (DEIM). So, in this paper, we discuss proper orthogonal decomposition (POD)-ROM LBM in the general form, present an appropriate matrix form for the LBM as explained, and implement POD or DEIM on that matrix form. In the end, the ability of this scheme is challenged with solving the urban air pollutant transition problem over some canyons areas as a practical problem.