A meshfree approach to non-Newtonian free surface ice flow: Application to the Haut Glacier d'Arolla

Numerical models of glacier and ice sheet dynamics traditionally employ nite difference or nite element methods. Although these are highly developed and mature methods, they su er from some drawbacks, such as inability to handle complex geometries ( nite di erences) or a costly assembly procedure for nonlinear problems ( nite elements). Additionally, they are mesh-based, and therefore moving domains become a challenge. In this paper, we introduce a novel meshfree approach based on a radial basis function (RBF) method. The meshfree nature of RBF methods enables e cient handling of moving margins and free ice surface. RBF methods are also highly accurate, easy to implement, and allow for reduction the computational cost associated with the linear system assembly, since stated in strong form. To demonstrate the global RBF method we model the velocity eld of ice ow in the Haut Glacier d'Arolla, which is governed by the nonlinear Stokes equations. We test the method for di erent basal conditions and for a free moving surface. We also compare the global RBF method with its localized counterpart the RBF partition of unity method (RBF PUM) that allows for a signi cant gain in the computational e ciency. We nd that the RBF methods are well suited for ice dynamics modelling, especially the partition of unity approach.