New design features of future reactors are being developed to ensure the integrity of the reactors under severe accident conditions. These features include the spreading of corium with subsequent flooding and cooling. Numerical simulations are performed to reduce the number of necessary large-scale experiments with radioactive material. For this reason, the development, verification, and validation of simulation methods are important foci. A method for predicting three-dimensional free-surface flows of a single-component, incompressible Newtonian fluid is presented. The thermodynamics and discrete phase transitions are simulated also. In addition to the fluid, structural materials are considered as hydrodynamic obstacles and heat structures. The method is applied to several flow, heat transfer, and phase transition problems of water and glycerol and of cerrotru (low-melting Bi-Sn alloy), thermite, and corium melts. The predictions provide a satisfactory representation of the experimental data and analytical solutions. Different physical processes are analyzed, e.g., gravity waves, creeping flows, Bénard convection, and thermodynamic interactions of fluid, structural material, and surroundings. The method is applied to the layout and design of experiments and exvessel corium-retention devices in nuclear reactors.