Numerical solutions of the variational equations for sandpile dynamics

A variational form of the energy conservation equation is applied to derive a system of variational inequalities describing the dynamics of sandpile growth on an arbitrary rigid support surface due to an external source of granular material. Water transport through the river networks and formation of lakes is also investigated as a limiting case of the sandpile evolution problem. A numerical algorithm is suggested for the solution of the obtained system of variational inequalities. The developed numerical procedure is applied for the investigation of the pile growth on a number of rigid support surfaces, water transport, and formation of lakes.