A smoothed particle hydrodynamics non-Newtonian model for ice sheet and ice shelf dynamics

Mathematical modeling of ice sheets is complicated by the non-linearity of the governing equations and boundary conditions. Standard grid-based methods require complex front tracking techniques and have limited capability to handle large material deformations and abrupt changes in bottom topography. As a consequence, numerical methods are usually restricted to shallow ice sheet and ice shelf approximations. We propose a new smoothed particle hydrodynamics (SPH) non-Newtonian model for coupled ice sheet and ice shelf dynamics. SPH, a fully Lagrangian particle method, is highly scalable and its Lagrangian nature and meshless discretization are well suited to the simulation of free surface flows, large material deformation, and material fragmentation. In this work, a fully 3D SPH model is used to study ice sheet/ice shelf behavior, and the dynamics of the grounding line. We investigate the dependence of the position of the grounding line on different factors, e.g., bedrock topography and bedrock slopes. In the proposed SPH model, we solve the full momentum and mass conservation equations, subject to the free surface boundary condition at the ice/water interface and the no-slip boundary condition at the ice/rock interface. The numerical accuracy of the SPH algorithm is verified by simulating the plane shear flows and the propagation of a blob of ice along a horizontal surface driven by gravity. Glen's flow law is used as the constitutive law for the ice behavior.