A moving-mesh splitting scheme for 2-dimensional quenching problems

A novel moving-mesh adaptive finite difference method is proposed for solving 2-dimensional quenching differential equations of the form u_t = u_xx + u_yy + (κ – u)^–2. Splitting strategies equipped with proper arc-length adaptations are utilized to achieve the computational efficiency as well as accuracy of the numerical solution of the potentially singular problems. Important results including the monotonicity of the nonlinear finite difference scheme are given. Simulation validations are provided to further demonstrate our conclusions. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)