This issuePrevious ArticleA Non-Self-Adjoint Quadratic Eigenvalue Problem
Describing a Fluid-Solid Interaction
Part II: Analysis of ConvergenceNext ArticleOn the asymptotic behavior of elliptic, anisotropic singular
A Numerical Method for a Non-Smooth Advection-Diffusion Problem Arising in Sand Mechanics
An operator-splitting algorithm is presented for the solution of a partial differential equation arising in the modeling of deposition processes in sand mechanics.
Sand piles evolution is modeled by an advection-diffusion equation, with a non-smooth diffusion operator that contains a point-wise constraint on the gradient of the solution.
Piecewise linear finite elements are used for the discretization in space.
The advection operator is treated with a stabilized SUPG finite element method.
An augmented Lagrangian method is proposed for the discretization of the fast/slow non-smooth diffusion operator.
A penalization approach, together with a Newton method, is used for the treatment of inequality constraints.
Numerical results are presented for the simulation of sand piles on flat and non-flat surfaces, and for extensions to water flows.