A Lattice Boltzmann Method for Electromagnetic Wave Propagation in Medium

A detailed measurement of rainfall is an important input to various climate models. Accuracy of rainfall measurements also has a socio-economic impact since it forms an important constituent in the region-wise and seasonal water budget. Radar measurements are most promising in this direction since they provide the detailed spatio-temporal data than any conventional method. However, it also has the disadvantage that rainfall estimation using radar is an indirect measurement and often involves the use of a number of correlations. The amount of scattered radiation is directly related to the raindrop size and shape distribution. Therefore, this project is aimed at solving Maxwell’s equations of electromagnetism using the lattice Boltzmann method with the intention of accurately relating the size and shape distribution of falling raindrops to scattered intensity and thus improving the rainfall measurement. Towards this objective, a D3Q7 code for a pseudo vector discrete Boltzmann distribution function has been developed following the work of Hauser and Verhey (2017) [1]. Standard validations involving scattering of electromagnetic waves by a dielectric interface and a circular scatterer have been performed. Error in the solutions was found to be minimal on comparing with analytical solutions. The applicability of the proposed numerical method towards analyzing scattering of electromagnetic waves by a three-dimensional scatterer, modelled on realistic hydrometeors, will be discussed..

I. Introduction

The equation of lattice Boltzmann was developed for fluid mechanics simulation. This numerical method is known as lattice Boltzmann method, like other conventional method finite difference time domain, LBM is efficient and alternate method and for implementation of boundary condition for complex geometry is easy in LBM [2]. Later on studies of LBM applied to simulate the heat transfer, multi component fluids, acoustics problems.