The present work focuses on the solution of fluid-structure interaction problems involving free surfaces and deformable structures. Free-surface flows are often encountered in reality, but the numerical solution of such problems remains a challenge, especially when the flow interacts with some flexible structure. The Particle Finite Element Method (PFEM) is nowadays a well-established Lagrangian method for the study of free-surface flows. The key feature of this method is the continuous remeshing of the computational domain through an efficient Delaunay triangulation, based on which the equations are solved using classical Finite Elements. In this work, the PFEM is coupled to Metafor, an in-house non-linear Finite Element solver, through an original partitioned strategy, based on block Gauss-Seidel iterations with dynamic relaxation. The main advantages of using a partitioned approach are that independent formulations can be employed for the fluid and the solid domains, and that the capabilities of already existing codes can be exploited at their best. In particular, in the problems proposed in this work, the solid structures can undergo very large deformations, and complex material laws, including plasticity for instance, can be easily taken into account. The techniques developed in this work are assessed through many examples, ranging from civil engineering problems, such as a dam break against a deformable obstacle, to aerospace applications, such a bird strike. Results are compared to those available in the literature, whenever possible.

As well known, the imposition of boundary conditions is, in many cases, the trickiest part in solving differential problems, both from a physical and numerical standpoint. This work focuses on the way boundary conditions are accounted for in the solution of fluid-structure interaction problems using the Particle Finite Element Method (PFEM). In particular, the PFEM traditionally employs no-slip conditions on the fluid-solid interfaces. Our aim is twofold. On the one hand, we demonstrate that, in the framework of the PFEM, the no-slip hypothesis is too strong in some cases, leading to erroneous physical results, and that a free-slip condition is to be preferred instead; we therefore propose two novel ways to impose free-slip conditions, devoting special attention to generality, simplicity and robustness. On the other hand, we show how the use of free-slip boundary conditions can also be beneficial with regards to two major problems arising from the remeshing procedure employed by the PFEM: the violation of the mass conservation principle and the introduction of spurious pressure oscillations.

Modal analysis, i.e., the computation of vibration modes of linear systems, is really quite sophisticated and advanced. Even though modal analysis served, and is still serving, the structural dynamics community for applications ranging from bridges to satellites, it is commonly accepted that nonlinearity is a frequent occurrence in engineering structures. Because modal analysis fails in the presence of nonlinear dynamical phenomena, the development of a practical nonlinear analog of modal analysis is the objective of this research. Progress in this direction has been made recently with the development of numerical techniques (harmonic balance, continuation of periodic solutions) for the computation of nonlinear normal modes (NNMs). Because these methods consider the conservative system, this study targets the computation of NNMs for nonconservative systems, i.e. defined as invariant manifolds in phase space. Specifically, a new finite element technique is proposed to solve the set of partial differential equations governing the manifold geometry. The algorithm is demonstrated using different two-degree-of-freedom systems.

In this paper, we present a general consistent numerical formulation able to take into account strain rate, damage and thermal effects of the material behaviour. A thermomechanical implicit approach for element erosion to model material failure is also presented. This approach can be applied both to ductile fracture for metals, relying on a continuum damage mechanics approach, coupled to different fracture criteria, as well as composite material failure described with either a failure criterion or a progressive damage model. The numerical models will be illustrated by different quasi-static and high strain rate applications for both metallic alloys and composite materials. All these physical phenomena have been included in an implicit dynamic object-oriented finite element code (implemented at LTAS-MN²L, University of Liège, Belgium) named Metafor [1].

The aim of this paper is to simulate low Mach number unsteady viscous flows using a density-based finite volumes solver. This kind of solver is known to encounter some difficulties to simulate low Mach number flows in which the density is almost constant. Convergence fails or accuracy decreases when the speed of sound is much greater than the fluid velocity. Local preconditioning methods intend to solve this problem by altering the time derivative terms of the Navier-Stokes equations in order to artificially modify the speed of sound, improving the convergence and accuracy in the case of low Mach number steady flows.

As well known, in the analysis of bird impact events the bird is often reduced, even experimentally, to a surrogate projectile modeled as a weakly compressible fluid (typically a mixture of water and air). From a numerical standpoint, the presence of a free surface and the strong interaction with the aircraft structures represent a limit for traditional computational fluid dynamics methods based on an Eulerian grid. On the other hand, classical Lagrangian methods cannot cope with the extremely large deformations experienced by the projectile during the impact. The Particle Finite Element Method (PFEM) is a Lagrangian particle method that can account for very large deformations, preserving the robustness and generality of the finite element method, and thus owning a key advantage over other approaches, e.g. Smoothed Particle Hydrodynamics (SPH), usually cursed with consistency and stability issues. To assess the possibilities of the method in the context of bird impact, theoretical analyses are initially performed based on the impact of a water jet on a rigid surface. Then, the influence of the geometry of a more realistic projectile is analyzed and the capability of the method to take into account separation and fragmentation is highlighted.

This paper addresses the numerical computation of nonlinear normal modes defined as two-dimensional invariant manifolds in phase space. A novel finite-element-based algorithm, combining the streamline upwind Petrov-Galerkin method with mesh moving and domain prediction-correction techniques, is proposed to solve the manifold-governing partial differential equations. It is first validated using conservative examples through the comparison with a reference solution given by numerical continuation. The algorithm is then demonstrated on nonconservative examples.

This paper presents a density-based finite volumes method for solving the unsteady Navier-Stokes equations on 3D unstructured grids. The second order Crank-Nicolson scheme is applied to perform the time integration. At each time step, the system of non linear equations is solved by means of a fully implicit dual time stepping method.An eigenvalues analysis demonstrates that this system can be ill-conditioned in the case of low Mach number flows for a certain range of CFL numbers. A new unsteady preconditioning technique, taking the CFL number into account, is proposed to improve convergence and accuracy. A second order and first order discretization schemes of the advective and viscous terms respectively are applied. The advective upwinding is performed by the AUSM+up scheme. The latter is modified to achieve robustness and accuracy for all Mach and CFL numbers.