Unified Lagrangian Formulation for Fluid and Solid Mechanics, Fluid-Structure Interaction and Coupled Thermal Problems Using the PFEM

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.- 3.1Stabilized 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.