Unified Lagrangian formulation for fluid and solid mechanics, fluid-structure interaction and coupled thermal problems using the PFEM

by Alessandro Franci

Institution: Universitat Politècnica de Catalunya
Year: 2015
Record ID: 1124793
Full text PDF: http://hdl.handle.net/10803/291562


The objective of this thesis is the derivation and implementation of a unified Finite Element formulation for the solution of uid and solid mechanics, Fluid-Structure Interaction (FSI) and coupled thermal problems. The unified procedure is based on a stabilized velocity-pressure Lagrangian formulation. Each time step increment is solved using a two-step Gauss-Seidel scheme: first the linear momentum equations are solved for the velocity increments, next the continuity equation is solved for the pressure in the updated configuration. The Particle Finite Element Method (PFEM) is used for the fluid domains, while the Finite Element Method (FEM) is employed for the solid ones. As a consequence, the domain is remeshed only in the parts occupied by the fluid. Linear shape functions are used for both the velocity and the pressure fields. In order to deal with the incompressibility of the materials, the formulation has been stabilized using an updated version of the Finite Calculus (FIC) method. The procedure has been derived for quasi-incompressible Newtonian fluids. In this work, the FIC stabilization procedure has been extended also to the analysis of quasi-incompressible hypoelastic solids. Specific attention has been given to the study of free surface flow problems. In particular, the mass preservation feature of the PFEM-FIC stabilized procedure has been deeply studied with the help of several numerical examples. Furthermore, the conditioning of the problem has been analyzed in detail describing the effect of the bulk modulus on the numerical scheme. A strategy based on the use of a pseudo bulk modulus for improving the conditioning of the linear system is also presented. The unified formulation has been validated by comparing its numerical results to experimental tests and other numerical solutions for fluid and solid mechanics, and FSI problems. The convergence of the scheme has been also analyzed for most of the problems presented. The unified formulation has been coupled with the heat tranfer problem using a staggered scheme. A simple algorithm for simulating phase change problems is also described. The numerical solution of several FSI problems involving the temperature is given. The thermal coupled scheme has been used successfully for the solution of an industrial problem. The objective of study was to analyze the damage of a nuclear power plant pressure vessel induced by a high viscous fluid at high temperature, the corium. The numerical study of this industrial problem has been included in the thesis.; El objectivo de la presente tesis es la derivación e implementación de una formulación unificada con elementos finitos para la solución de problemas de mecánica de fluidos y de sólidos, interacción fluido-estructura (Fluid-Structure Interaction (FSI)) y con acoplamiento térmico. El método unificado està basado en una formulación Lagrangiana estabilizada y las variables incognitas son las velocidades y la presión. Cada paso de tiempo se soluciona a través de un esquema de dos pasos de tipo Gauss-Seidel. Primero…