An integral equation method and an asymptotic analysis approach for erosion in porous media

In nature, erosion caused by water or air flow is one of the most prevalent

geological and mechanical processes. This phenomenon occurs at the fluid-solid 

interface when the total shear stress induced by the flow exceeds specific 

critical threshold that depends on the properties of the solid material. 

This research project focuses on the mathematical modeling and simulation 

of erosion process in a porous medium characterized by axisymmetric channels. 

We employ an integral equation method, which enables efficient and accurate 

analysis of the erosion process within the porous medium. We present a detailed 

comparison between the numerical solutions from our model and the reduced 

mathematical model using asymptotic analysis developed by Kahza and Sanaei 

[Phys. Rev. Fluids, 9(2024)], providing insights into erosion patterns and 

validating the proposed approach. Furthermore, we extend our methodology to 

examine the transport and behavior of active particles immersed in the fluid.