Modeling calving process of glacier with dilated polyhedral discrete element method

Mass loss caused by glacier calving is one of the direct contributors to global sea level rise.Reliable calving laws are required for accurate modelling of ice sheet mass balance.Both continuous and discontinuous methods have been used for glacial calving simulations.In this study,the discrete element method(DEM)based on dilated polyhedral elements is introduced to simulate the calving process of a tidewater glacier.Dilated polyhedrons can be obtained from the Minkowski sum of a sphere and a core polyhedron.These elements can be utilized to generate a continuum ice material,where the interaction force between adjacent elements is modeled by constructing bonds at the joints of the common faces.A hybrid fracture model considering fracture energy is introduced.The viscous creep behavior of glaciers on long-term scales is not considered.By applying buoyancy and gravity to the modelled glacier,DEM results show that the calving process is caused by cracks which are initialized at the top of the glacier and spread to the bottom.The results demonstrate the feasibility of using the dilated polyhedral DEM method in glacier simulations,additionally allowing the fragment size of the breaking fragments to be counted.The relationship between crack propagation and internal stress in the glacier is analyzed during calving process.Through the analysis of the Mises stress and the normal stress between the elements,it is found that geometric changes caused by the glacier calving lead to the redistribution of the stress.The tensile stress between the elements is the main influencing factor of glacier ice failure.In addition,the element shape,glacier base friction and buoyancy are studied,the results show that the glacier model based on the dilated polyhedral DEM is sensitive to the above conditions.

High Order Schemes on Three-Dimensional General Polyhedral Meshes—Application to the Level Set Method

In this article,we detail the methodology developed to construct arbitrarily high order schemes—linear and WENO—on 3D mixed-element unstructured meshes made up of general convex polyhedral elements.The approach is tailored specifically for the solution of scalar level set equations for application to incompressible two-phase flow problems.The construction of WENO schemes on 3D unstructured meshes is notoriously difficult,as it involves a much higher level of complexity than 2D approaches.This due to the multiplicity of geometrical considerations introduced by the extra dimension,especially on mixed-element meshes.Therefore,we have specifically developed a number of algorithms to handle mixed-element meshes composed of convex polyhedra with convex polygonal faces.The contribution of this work concerns several areas of interest:the formulation of an improved methodology in 3D,the minimisation of computational runtime in the implementation through the maximum use of pre-processing operations,the generation of novel methods to handle complex 3D mixed-element meshes and finally the application of the method to the transport of a scalar level set.