Tretyak V. Methods and means of mathematical simulation of heat transfer in two-phase environment (by the example of laser-arc welding)

The dissertation is devoted to the mathematical models, effective adaptive methods and computer simulation of thermal processes in two-phase two-layer environment (by the example of laser- arc welding) tools development. The features of the simulation object are a variable form; potential phase transition; locality, high power and velocity of the heating elements. The mathematical model is formulated as a boundary problem for unsteady three-dimensional nonlinear partial differential equations defined in the variable domain. The nonlinearity of the problem is caused by the temperature dependence of the volumetric heat capacity for which the linear- exponential approximation is proposed. The method of simulation that provides accounting features of the process and conditions of phase transitions in discrete time at the correct discretization schemes for solution of the Stefan problem in enthalpy formulation by finite differences method is proposed. A method of adaptive mesh generation improved through: taking into account the rate of convergence of iterative processes of solving systems of nonlinear difference equations by numerical sensor; phase of the previous calculations, which solves the problem of inconsistency of mesh refinement and high gradients zones. Balance Method is extended to problems with discontinuous time derivative held coefficient.