Online estimation of inlet contaminant concentration using Eulerian-Lagrangian method of fundamental solutions and Bayesian inference

The advection-diffusion equation is fundamental to modeling various transport phenomena, including the distribution of chemical species in surface or groundwater flow. In cases where the concentration at the source is unknown, inverse problem formulations are required to estimate the desired states by assimilating concentration monitoring data from specific points along the watercourse using a Bayesian approach. This paper proposes a combination of the Eulerian-Lagrangian method and the meshless method of fundamental solutions to solve the advection-diffusion equation. Moreover, the method was used as an evolution model for the sequential importance resampling particle filter algorithm to reconstruct the time-dependent inlet pollutant concentration in inverse problems. Numerical smooth and discontinuous inlet function results show that the particle filter - Eulerian-Lagrangian method of fundamental solutions combination can reconstruct inlet concentration time series.