Mathematical Modelling and Analysis 2005. Pages 473–478 Proceedings of the 10 th International Conference MMA2005&CMAM2, Trakai c  2005 Technika ISBN 9986-05-924-0 DYNAMIC ADAPTATION METHOD FOR MODELLING OF MELTING AND EVAPORATION PROCESSES WITH CONVECTION V.I. MAZHUKIN 1 , M.M. CHUIKO 2 and A.M LAPANIK 3 1 Institute of Mathematical Modelling, RAS Miusskaya Sq. 4, 125047 Moscow, Russia 2 Institute of Mathematics, NAS of Belarus Surganov Str. 11, 220072 Minsk, Belarus E-mail: chuiko@im.bas-net.by 3 Belarussian State University Nezavisimosti Ave. 4, 220050 Minsk, Belarus E-mail: alapanik@tut.by Abstract. The application of the dynamic adaptation method for the explicit tracking of interfaces in two-dimensional phase change problems with convection is presented. The results of computational experiments in modelling the action of high energy fluxes on metal target are given. Key words: Stefan problem, natural convection, melting, evaporation, adaptive method, curvilinear coordinate systems, difference scheme 1. Introduction Concentrated energy fluxes are wide-spread tools for the treatment of different materials. Laser and electron-beam techniques are used in many technological operations, such as drilling, cutting, welding and so on. Most of the applica- tions for laser irradiation are connected with the phase transformations of metals, dielectrics and semiconductors (melting-crystallization and evapora- tion processes). The main feature of such processes is the presence of moving interfaces where phase changes occur. Due to the complexity of the problem the numerical methods are used for its study [5]. Two alternative approaches are widely used for numerical solution of phase transition (or Stefan-like) problems: explicit tracking of moving interfaces [1]