JST Presto Symposium on Mathematical Sciences towards Environmental Problems

The numerical simulation of the motion of Rhone’s glacier in the Swiss Alps is performed from 1874 to 2007, and then from 2007 to 2100. Given the shape of the glacier, the velocity of ice u is obtained by solving a 3D nonlinear Stokes problem. Then, the shape of the glacier is updated by computing the volume fraction of ice φ, which satisfies the transport equation ∂φ ∂t + u · ∇φ = bδΓA . Here bδΓA is a source term acting only on the ice-air interface ΓA which accounts for the accumulation or ablation of ice due to snow falls or melting. A decoupling algorithm allows the two above problems to be solved using different numerical techniques. The nonlinear Stokes problem is solved on a fixed, unstructured finite element mesh made of tetrahedrons. The transport equation is solved using a fixed, structured grid made of smaller cells. The numerical simulation is performed between 1874 and 2007. Then, a median climatic scenario is considered in order to predict the shape of the glacier from 2007 until 2100. 1 Supported by the Swiss National Science Foundation

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