1 Introduction -- 1.1 Objectives -- 1.2 State of the art -- 1.2.1 Eulerian and Lagrangian approaches for free surface flow analysis -- 1.2.2 Stabilization techniques -- 1.2.3 Algorithms for FSI problems -- 1.3 Numerical model -- 1.3.1 Reasons -- 1.3.2 Essential features -- 1.3.3 Outline -- 1.4 Publications -- 2 Velocity-based formulations for compressible materials -- 2.1 Velocity formulation -- 2.1.1 From the local form to the spatial semi-discretization -- 2.1.2 Time integration -- 2.1.3 Linearization -- 2.1.4 Incremental solution scheme -- 2.2 Mixed velocity-pressure formulation -- 2.2.1 Quasi-incompressible form of the continuity equation -- 2.2.2 Solution method -- 2.3 Hypoelasticity -- 2.3.1 Velocity formulation for hypoelastic solids -- 2.3.2 Mixed Velocity-Pressure formulation for hypoelastic solids -- 2.3.3 Theory of plasticity -- 2.3.3.1 Hypoelastic-plastic materials -- 2.3.4 Validation examples -- 2.4 Summary and conclusions -- 3 Unified stabilized formulation for quasi-incompressible materials -- 3.1 Stabilized FIC form of the mass balance equation -- 3.1.1 Governing equations -- 3.1.2 FIC mass balance equation in space and in time -- 3.1.3 FIC stabilized local form of the mass balance equation -- 3.1.4 Variational form -- 3.1.5 FEM discretization and matrix form -- 3.2 Solution scheme for quasi-incompressible Newtonian fluids -- 3.2.1 Governing equations -- 3.2.2 Solution scheme -- 3.3 Solution scheme for quasi-incompressible hypoelastic solids -- 3.4 Free surface flow analysis -- 3.4.1 The Partiele Finite Element Method -- 3.4.1.1 Remeshing -- 3.4.1.2 Basic steps -- 3.4.1.3 Advantages and disadvantages -- 3.4.2 Mass conservation analysis -- 3.4.2.1 Numerical examples -- 3.4.3 Analysis of the conditioning of the solution scheme -- 3.4.3.1 Drawbacks associated to the real bulk modulus -- 3.4.3.2 Optimum value for the pseudo bulk modulus -- 3.4.3.3 Numerical examples -- 3.5 Validation examples -- 3.5.1 Validation of the Unified formulation for Newtonian fluids -- 3.5.2 Validation of the Unified formulation for quasi-incompressible hypoelastic solids -- 3.6 Summary and conclusions -- 4 Unified formulation for F SI problems -- 4.1 Introduction -- 4.2 FSI algorithm -- 4.3 Coupling with the Velocity formulation for the solid -- 4.4 Coupling with the mixed Velocity-Pressure formulation for the solid -- 4.5 Numerical examples -- 4.6 Summary and conclusions -- 5 Coupled thermal-mechanical formulation -- 5.1 Introduction -- 5.2 Heat problem -- 5.2.1 FEM discretization and solution for a time step -- 5.3 Thermal coupling -- 5.3.1 Numerical examples -- 5.4 Phase change -- 5.4.1 Numerical example: melting of an ice block -- 5.5 Summary and conclusions -- 6 Industrial application: PFEM Analysis Model of NPP Severe Accident -- 6.1 Introduction -- 6.1.1 Assumptions allowed by the specification -- 6.2 Numerical method -- 6.3 Basic Model -- 6.3.1 Problem data -- 6.3.2 Preliminary study -- 6.3.3 Numerical results -- 6.4 Detailed model -- 6.4.1 Problem data -- 6.4.2 Preliminary study -- 6.4.3 Numerical results -- 6.5 Summary and conclusions -- 7 Conclusions and future lines of research -- 7.1 Contributions -- 7.2 Lines for future work.