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The pseudo‐concentration method is applied to the analysis of transient processes. A simple, easy‐to‐handle model is obtained by keeping an Eulerian description: it does not require remeshing after a certain amount of plastic deformation. The range of applicability of the method is extended to non‐confined (even with several free surfaces) processes. It is shown the need of distinct handling of free surfaces according to their orientation to the direction of the flow. A seamless tube rolling process, a cylinder upsetting and a backward extrusion are modelled. Experimental data and results obtained by other methods are used to compare and discuss the performance of the model.

The purpose of this paper is to evaluate the possibilities of the particle finite element method for simulation of free surface flows.

A numerical simulation of a number of examples for which experimental data are available is performed. The simulations are run using the same scale as the experiment in order to minimize errors due to scale effects. Some examples are chosen from the civil engineering field: a study of the flow over a flip bucket is analyzed for both 2D and 3D models, and the flow under a planar sluice gate is studied in 2D. Other examples, such as a 2D and 3D “dam break” with an obstacle are taken from the smooth particle hydrodynamics literature.

Different scenarios are simulated by changing the boundary conditions for reproducing flows with the desired characteristics. Different mesh sizes are considered for evaluating their influence on the final solution.

Details of the input data for all the examples studied are given. The aim is to identify benchmark problems for future comparisons between different numerical approaches for free surface flows.

Addresses two difficulties which arise when using a compressible code with equal order interpolation (non‐staggered grids in the finite‐difference nomenclature) to capture a steady‐state solution in the incompressible limit, i.e. at low Mach numbers. Explains that, first, numerical instabilities in the form of spurious oscillations in pressure pollute the solution and, second, the convergence to the steady state becomes extremely slow owing to bad conditioning of the different speeds of propagation. By using a stabilized method, allows the use of equal‐order interpolations in a consistent (weighted‐residual) formulation which stabilizes both the convection and the continuity terms at the same time. On the other hand, by using specially devised preconditioning, assures a rate of convergence independent of Mach number.

The purpose of this paper is to highlight the possibilities of a novel Lagrangian formulation in dealing with the solution of the incompressible Navier‐Stokes equations with very large time steps.

The design of the paper is based on introducing the origin of this novel numerical method, originally inspired on the Particle Finite Element Method (PFEM), summarizing the previously published theory in its moving mesh version. Afterwards its extension to fixed mesh version is introduced, showing some details about the implementation.

The authors have found that even though this method was originally designed to deal with heterogeneous or free‐surface flows, it can be competitive with Eulerian alternatives, even in their range of optimal application in terms of accuracy, with an interesting robustness allowing to use large time steps in a stable way.

With this objective in mind, the authors have chosen a number of benchmark examples and have proved that the proposed algorithm provides results which compare favourably, both in terms of solution time and accuracy achieved, with alternative approaches, implemented in in‐house and commercial codes.

Large deformation problems are frequently encountered in various fields of geotechnical engineering. The particle finite element method (PFEM) has been proven to be a promising method to solve large deformation problems. This study aims to develop a computational framework for modelling the hydro-mechanical coupled porous media at large deformation based on the PFEM.

The PFEM is extended by adopting the linear and quadratic triangular elements for pore water pressure and displacements. A six-node triangular element is used for modelling two-dimensional problems instead of the low-order three-node triangular element. Thus, the numerical instability induced by volumetric locking is avoided. The Modified Cam Clay (MCC) model is used to describe the elasto-plastic soil behaviour.

The proposed approach is used for analysing several consolidation problems. The numerical results have demonstrated that large deformation consolidation problems with the proposed approach can be accomplished without numerical difficulties and loss of accuracy. The coupled PFEM provides a stable and robust numerical tool in solving large deformation consolidation problems. It is demonstrated that the proposed approach is intrinsically stable.

The PFEM is extended to consider large deformation-coupled hydro-mechanical problem. PFEM is enhanced by using a six-node quadratic triangular element for displacement and this is coupled with a four-node quadrilateral element for modelling excess pore pressure.

An original finite element scheme for advection‐diffusion‐reaction problems is presented. The new method, called spotted Petrov‐Galerkin (SPG), is a quadratic Petrov‐Galerkin (PG) formulation developed for the solution of equations where either reaction (associated to zero‐order derivatives of the unknown) and/or advection (proportional to first‐order derivatives) dominates on diffusion (associated to second‐order derivatives). The addressed issues are turbulence and advective‐reactive features in modelling turbomachinery flows.

The present work addresses the definition of a new PG stabilization scheme for the reactive flow limit, formulated on a quadratic finite element space of approximation. We advocate the use of a higher order stabilized formulation that guarantees the best compromise between solution stability and accuracy. The formulation is first presented for linear scalar one‐dimensional advective‐diffusive‐reactive problems and then extended to quadrangular Q2 elements.

The proposed advective‐diffusive‐reactive PG formulation improves the solution accuracy with respect to a standard streamline driven stabilization schemes, e.g. the streamline upwind or Galerkin, in that it properly accounts for the boundary layer region flow phenomena in presence of non‐equilibrium effects.

The numerical method here proposed has been designed for second‐order quadrangular finite‐elements. In particular, the Reynolds‐Averaged Navier‐Stokes equations with a non‐linear turbulence closure have been modelled using the stable mixed element pair Q2‐Q1.

This paper investigated the predicting capabilities of a finite element method stabilized formulation developed for the purpose of solving advection‐reaction‐diffusion problems. The new method, called SPG, demonstrates its suitability in solving the typical equations of turbulence eddy viscosity models.

This study aims to evaluate blast loads on and the response of submerged structures.

An arbitrary Lagrangian–Eulerian method is developed to model fluid–structure interaction (FSI) problems of close-in underwater explosions (UNDEX). The “fluid” part provides the loads for the structure considers air, water and high explosive materials. The spatial discretization for the fluid domain is performed with a second-order vertex-based finite volume scheme with a tangent of hyperbola interface capturing technique. The temporal discretization is based on explicit Runge–Kutta methods. The structure is described by a large-deformation Lagrangian formulation and discretized via finite elements. First, one-dimensional test cases are given to show that the numerical method is free of mesh movement effects. Thereafter, three-dimensional FSI problems of close-in UNDEX are studied. Finally, the computation of UNDEX near a ship compartment is performed.

The difference in the flow mechanisms between rigid targets and deforming targets is quantified and evaluated.

Cavitation is modeled only approximately and may require further refinement/modeling.

The results demonstrate that the proposed numerical method is accurate, robust and versatile for practical use.

Better design of naval infrastructure [such as bridges, ports, etc.].

To the best of the authors’ knowledge, this study has been conducted for the first time.

The purpose of this paper is to apply the Peridynamic differential operator (PDDO) to incompressible inviscid fluid flow with moving boundaries. Based on the potential flow theory, a Lagrangian formulation is used to cope with non-linear free-surface waves of sloshing water in 2D and 3D rectangular and square tanks.

In fact, PDDO recasts the local differentiation operator through a nonlocal integration scheme. This makes the method capable of determining the derivatives of a field variable, more precisely than direct differentiation, when jump discontinuities or gradient singularities come into the picture. The issue of gradient singularity can be found in tanks containing vertical/horizontal baffles.

The application of PDDO helps to obtain the velocity field with a high accuracy at each time step that leads to a suitable geometry updating for the procedure. Domain/boundary nodes are updated by using a second-order finite difference time algorithm. The method is applied to the solution of different examples including tanks with baffles. The accuracy of the method is scrutinized by comparing the numerical results with analytical, numerical and experimental results available in the literature.

Based on the investigations, PDDO can be considered a reliable and suitable approach to cope with sloshing problems in tanks. The paper paves the way to apply the method for a wider range of problems such as compressible fluid flow.

A non‐linear shallow thin shell element is described. The element is a curved quadrilateral one with corner nodes only. At each node, six degrees of freedom (i.e. three translations and three rotations) make the element easy to connect to space beams, stiffeners or intersecting shells. The curvature is dealt with by Marguerre's theory. Membrane bending coupling is present at the element level and improves the element behaviour, especially in non‐linear analysis. The element converges to the deep shell solution. The sixth degree of freedom is a true one, which can be assimilated to the in‐plane rotation. The present paper describes how overstiffness due to membrane locking on the one hand and to the sixth degree of freedom on the other hand can be corrected without making use of numerical adjusted factors. The behaviour of this new element is analysed in linear and non‐linear static and dynamic tests.

This paper aims to report the study of a fluid buoy system that includes wave effects, with particular emphasis on validating the numerical results with experimental data.

A fluid–solid coupled algorithm is proposed to describe the motion of a rigid buoy under the effects of waves. The Navier–Stokes equations are solved with the open-source finite volume package Code Saturne, in which a free-surface capture technique and equations of motion for the solid are implemented. An ad hoc experiment on a laboratory scale is built. A buoy is placed into a tank partially filled with water; the tank is mounted into a shake table and subjected to controlled motion that promotes waves. The experiment allows for recording the evolution of the free surface at the control points using the ultrasonic sensors and the movement of the buoy by tracking the markers by postprocessing the recorded videos. The numerical results are validated by comparison with the experimental data.

The implemented free-surface technique, developed within the framework of the finite-volume method, is validated. The best-obtained agreement is for small amplitudes compatible with the waves evolving under deep-water conditions. Second, the algorithm proposed to describe rigid-body motion, including wave analysis, is validated. The numerical body motion and wave pattern satisfactorily matched the experimental data. The complete 3D proposed model can realistically describe buoy motions under the effects of stationary waves.

The novel aspects of this study encompass the implementation of a fluid–structure interaction strategy to describe rigid-body motion, including wave effects in a finite-volume context, and the reported free-surface and buoy position measurements from experiments. To the best of the authors’ knowledge, the numerical strategy, the validation of the computed results and the experimental data are all original contributions of this work.