Symmetry analysis, optimal system, and invariant solutions for a (2+1)-dimensional two-phase mass flow model

The paper investigates a two-phase mass flow model governed by gravity, involving solid particles and a viscous fluid. By utilizing the Lie symmetries admitted by the system, similarity solutions for the (2+1)-dimensional two-phase mass flow model are obtained. A comprehensive set of local point symmetries is established, and a well-suited collection of two-dimensional subalgebras is constructed from the maximal Lie invariance algebra. The optimal system's vector fields are then utilized to directly reduce the governing model to a system of ordinary differential equations. Through analytical solutions, we successfully solve the resulting systems and further analyze their physical behaviors numerically.

Automated summary

This paper investigates a two-phase mass flow model governed by gravity, which involves solid particles and a viscous fluid. By utilizing the Lie symmetries admitted by the system, similarity solutions for the (2+1)-dimensional two-phase mass flow model are obtained. Through analytical solutions and numerical analysis, the physical behaviors of the resulting systems are successfully analyzed.