Gravity‐Driven Granular Flows in the Context of Advanced Symmetry Techniques

ABSTRACT This study investigates a granular flow model on an inclined plane characterized by a constant friction coefficient to describe gravity‐driven debris avalanches. We derive diverse sets of group‐invariant solutions by employing both classical and nonclassical symmetries of the Lie group. Among these, solutions to 1 and 2 rarefaction waves corresponding to the Riemann problem are highlighted. The significance of nonclassical symmetries is explicitly demonstrated in our analysis. Essential conservation laws are derived using the multiplier method and the system's nonlinear self‐adjointness. Additionally, we discuss the obtained solutions in the context of the evolution of weak discontinuity waves, and we derive new non‐group invariant solutions using the method of conservation laws.