Implementation of finite difference method based on explicit and Crank-Nicolson method to the thermomechanical ice sheet model

Thermomechanical ice sheet model is applied to simulate ice sheet behavior in the Antarctic region. The parameters involved are ice thickness, ice temperature and ice velocity. This model is proposed by Bueler (2012)[1]. It corresponding roughly to the two-dimensional European Ice Sheet Modeling Initiative (EISMENT) experiment and the thermomechanical coupling equation. Thus, the expression of thermomechanical coupling equations is quite simplified. The numerical discretization scheme for the model is explicit and Crank-Nicholson methods. The efficiency of the finite difference methods such as implicit, explicit and Crank-Nicholson methods for solving the partial differential equation (PDE) of thermomechanical ice sheet modeling is also determined. MATLAB has been choosing as the development platform for the implementations since it is well suited for the kind of computations required.