Institute of Fundamental Technological Research

In this work, we develop a new algorithm to solve large-scale incompressible time-dependent fluid-structure interaction problems using a matrix-free finite element method in arbitrary Lagrangian–Eulerian frame of reference. We derive a semi-implicit time integration scheme which improves the geometry-convective explicit scheme for problems involving the interaction between incompressible hyperelastic solids and incompressible fluids. The proposed algorithm relies on the reformulation of the time-discrete problem as a generalized Stokes problem with strongly variable coefficients, for which optimal preconditioners have recently been developed. The resulting algorithm is scalable, optimal, and robust: we test our implementation on model problems that mimic classical Turek-Hron benchmarks in two and three dimensions, and investigate timing and scalability results.

arbitrary Lagrangian-Eulerian, finite element method, fluid-structure interaction, geometric multigrid, matrix-free method, monolithic scheme

The aim of this study is to analyse the joint effect of reinforcement shape and packing on the effective behaviour of particulate composites. The proposed semi-analytical modelling method combines the Replacement Mori–Tanaka scheme, by means of which the concentration tensors for non-ellipsoidal inhomogeneities are found numerically, and the analytical morphologically representative pattern approach to account for particle packing. Five shapes of inhomogeneities are selected for the analysis: a sphere, a prolate ellipsoid, a sphere with cavities, an oblate spheroid with a cavity as well as an inhomogeneity created by three prolate spheroids crossing at right angles. Semi-analytical estimates are compared with the results of numerical simulations performed using the finite element method and with the outcomes of classical mean-field models based on the Eshelby solution, e.g. the Mori–Tanaka model or the self-consistent scheme.

composite material, micromechanics, computational modelling, packing effect, shape effect

In this paper we present a matrix-free multilevel solver for the generalized Stokes problem with discontinuous viscosity. The algorithm is based on the FGMRES iteration preconditioned with a block-smoothed multigrid method. Numerical experiments on unstructured grids indicate that for a broad range of smoother parameters, the convergence speed is only weakly dependent on both the number of unknowns and the jumps of the viscosity coefficient.

Stokes problem, Discontinuous coefficients, Multigrid, Matrix-free, Parallel computing

The unique properties of ceramic foams make them well suited to a range of applications in science and engineering such as heat transfer, reaction catalysis, flow stabilization, and filtration. Consequently, a detailed understanding of the transport properties (i.e. permeability, pressure drop) of these foams is essential. This paper presents the results of both numerical and experimental investigations of the morphology and pressure drop in 10 ppi (pores per inch), 20 ppi and 30 ppi ceramic foam specimens with porosity in the range of 75–79%. The numerical simulations were carried out using a GPU implementation of the three-dimensional, multiple-relaxation-time lattice Boltzmann method (MRT-LBM) on geometries of up to 360 million nodes in size. The experiments were undertaken using a water channel. Foam morphology (porosity and specific surface area) was studied on post-processed, computed tomography (CT) images, and the sensitivity of these results to CT image thresholding was also investigated. Comparison of the numerical and experimental data for pressure drop exhibited very good agreement. Additionally, the results of this study were verified against other researchers׳ data and correlations, with varying outcomes.

Ceramic foam, Pressure drop, Lattice Boltzmann method, Darcy–Forchheimer equation, Specific surface area, Pore-scale simulation

A mixed formulation of the mass-conserving cavitation model is developed. The cavitation problem is formulated in terms of the hydrodynamic pressure and a complementary variable representing the void fraction in the cavitation zone. Weak form of the mass-balance equation is consistently derived, and it exhibits subtle differences with respect to the available formulations. Finite element treatment preserves the two-field formulation, and a semi-smooth Newton method is applied to solve the resulting discretized equations. A monolithic Newton-based scheme is also applied to solve the fully coupled elastohydrodynamic lubrication problem in the soft-EHL regime. Numerical examples illustrate the performance of the computational scheme.

Lubrication, Cavitation, Reynolds equation, Soft-EHL problem