Computation of sand fluidization phenomena using stabilized finite elements

This paper is concerned with the phenomenon of sand fluidization that occurs when sand particles are dislodged from the solid matrix sharp fluid pressure and stress gradients. For modeling purposes, the problem can be cast within mixture theory in which solid, fluid and fluidized sand phases interact while being constrained by mass balance equations written for each of the phases. A sink term is introduced in the equations to describe the detachment of sand particles via an erosion law. Because of the complexity and physics of the problem, several challenges are encountered when solving the ensuing governing equations. Numerical instabilities in the form of node-to-node wiggles or oscillations corrupt the finite element solution of the governing equations, unless some stabilization is provided through the introduction of numerical damping/diffusion. This damping is not ad hoc, but it naturally emerges in the analysis when enriching the field variables with higher gradient terms. Some numerical examples are given to illustrate the effectiveness of such stabilization method.