A discontinuous Galerkin method for mathematical modeling of ice melting at the interaction with the environment

[摘要] A Stefan problem with a moving boundary in a heterogeneous two-phase medium is considered. For solving the Stefan problem, a discontinuous Galerkin method in a nonsymmetrical Inner Penalty formulation is used. We propose to split the problem solution into a discontinuous component in the phase transition zone and a continuous component outside the phase transition zone. A multiscale method allows to reduce a number of freedom degrees by using the discontinuous Galerkin method in the phase transition zone only. Mathematical modeling results of the ice melting at the interaction with the environment are given.

[发布机构] Trofimuk Institute of Petroleum Geology and Geophysics of SB RAS, Novosibirsk, Russia^1;Novosibirsk State Technical University, Russia^2

[效力级别] 力学 [学科分类] 力学，机械学

[关键词] Discontinuous Galerkin methods;Freedom degrees;Moving boundaries;Multiscale method;Penalty formulation;Problem solutions;Stefan problem;Two phase medium