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The spatial organization of active particles or swimmers may depend strongly on the nature of the interaction between the particles and the boundary. Here we use robotic fish of several centimeters dimensions that swim at high enough velocities to reach Reynolds numbers Re of order or . Under confinement in circular arenas filled with a shallow layer of water, these robots swim mostly near the walls and undergo a gradual transition from swirling motion near the boundaries to large cluster formation as the number of particles in the assembly is increased. This transition is highly dependent on the nature of the walls: for solid impermeable walls this transition occurs for small numbers of fish robots. For porous walls this transition is delayed and occurs at larger numbers. The main reason why the two boundaries affect the swimming differently is the alignment of the fish robots at the wall: for the impermeable boundary the fish robots align with a smaller angle to the wall while for the porous case, the fish robots align with a larger angle at the wall allowing the formation of linear clusters. We carry out numerical simulations of model fish in three dimensions to examine how such experimental results can be understood. The interest of these simulations is that they provide a direct and quantitative view of the properties of the flow engendered by the fish like objects. The interaction of this flow with other fish or with the boundaries is the crucial aspect behind the self organization. These simulations reproduce the main features of the behavior of the swimmers such as their swimming near the walls or their angle with respect to the boundary. By using flexible and free to move arenas in experiments and simulations, we show that the assembly of fish robots is capable of creating large deformations as well as induce mobility of the arenas through the self-organization of the robotic fish opening the possibility of making sub-aquatic flexible robots of robots.

An Eulerian method to numerically solve incompressible bifluid problems with high density ratio is presented. This method can be considered as an improvement of the Ghost Fluid method, with the specificity of a sharp second-order numerical scheme for the spatial resolution of the discontinuous elliptic problem for the pressure. The Navier–Stokes equations are integrated in time with a fractional step method based on the Chorin scheme and discretized in space on a Cartesian mesh. The bifluid interface is implicitly represented using a level-set function. The advantage of this method is its simplicity to implement in a standard monofluid Navier–Stokes solver while being more accurate and conservative than other simple classical bifluid methods. The numerical tests highlight the improvements obtained with this sharp method compared to the reference standard first-order methods.

Biofilms are spatially organized communities of microorganisms embedded in a self-produced organic matrix, conferring to the population emerging properties such as an increased tolerance to the action of antimicrobials. It was shown that some bacilli were able to swim in the exogenous matrix of pathogenic biofilms and to counterbalance these properties. Swimming bacteria can deliver antimicrobial agents in situ, or potentiate the activity of antimicrobial by creating a transient vascularization network in the matrix. Hence, characterizing swimmer trajectories in the biofilm matrix is of particular interest to understand and optimize this new biocontrol strategy in particular, but also more generally to decipher ecological drivers of population spatial structure in natural biofilms ecosystems. In this study, a new methodology is developed to analyze time-lapse confocal laser scanning images to describe and compare the swimming trajectories of bacilli swimmers populations and their adaptations to the biofilm structure. The method is based on the inference of a kinetic model of swimmer populations including mechanistic interactions with the host biofilm. After validation on synthetic data, the methodology is implemented on images of three different species of motile bacillus species swimming in a Staphylococcus aureus biofilm. The fitted model allows to stratify the swimmer populations by their swimming behavior and provides insights into the mechanisms deployed by the micro-swimmers to adapt their swimming traits to the biofilm matrix. Anyone who has ever cleaned a bathroom probably faced biofilms, the dark, slimy deposits that lurk around taps and pipes. These structures are created by bacteria which abandon their solitary lifestyle to work together as a community, secreting various substances that allow the cells to organise themselves in 3D and to better resist external aggression. Unwanted biofilms can impair industrial operations or endanger health, for example when they form inside medical equipment or water supplies. Removing these structures usually involves massive application of substances which can cause long-term damage to the environment. Recently, researchers have observed that a range of small rod-shaped bacteria – or ‘bacilli’ – can penetrate a harmful biofilm and dig transient tunnels in its 3D structure. These ‘swimmers’ can enhance the penetration of anti-microbial agents, or could even be modified to deliver these molecules right inside the biofilm. However, little is known about how the various types of bacilli, which have very different shapes and propelling systems, can navigate the complex environment that is a biofilm. This knowledge would be essential for scientists to select which swimmers could be the best to harness for industrial and medical applications. To investigate this question, Ravel et al. established a way to track how three species of bacilli swim inside a biofilm compared to in a simple fluid. A mathematical model was created which integrated several swimming behaviors such as speed adaptation and direction changes in response to the structure and density of the biofilm. This modelling was then fitted on microscopy images of the different species navigating the two types of environments. Different motion patterns for the three bacilli emerged, each showing different degrees of adapting to moving inside a biofilm. One species, in particular, was able to run straight in and out of this environment because it could adapt its speed to the biofilm density as well as randomly change direction. The new method developed by Ravel et al. can be redeployed to systematically study swimmer candidates in different types of biofilms. This would allow scientists to examine how various swimming characteristics impact how bacteria-killing chemicals can penetrate the altered biofilms. In addition, as the mathematical model can predict trajectories, it could be used in computational studies to examine which species of bacilli would be best suited in industrial settings.

We investigate the role of linear mechanisms in the emergence of nonlinear horizontal self-propelled states of a heaving foil in a quiescent fluid. Two states are analysed: a periodic state of unidirectional motion and a quasi-periodic state of slow back and forth motion around a mean horizontal position. The states emergence is explained through a fluid–solid Floquet stability analysis of the non-propulsive symmetric base solution. Unlike a purely hydrodynamic analysis, our analysis accurately determines the locomotion states onset. An unstable synchronous mode is found when the unidirectional propulsive solution is observed. The obtained mode has a propulsive character, featuring a mean horizontal velocity and an asymmetric flow that generates a horizontal force accelerating the foil. An unstable asynchronous mode, also featuring flow asymmetry and a non-zero velocity, is found when the back and forth state is observed. Its associated complex multiplier introduces a slow modulation of the flapping period, agreeing with the quasi-periodic nature of the back and forth regime. The temporal evolution of this perturbation shows how the horizontal force exerted by the flow is alternatively propulsive or resistive over a slow period. For both modes, an analysis of the velocity and force perturbation time-averaged over the flapping period is used to establish physical instability criteria. The behaviour for a large solid-to-fluid density ratio of the modes is thus analysed. The asynchronous fluid–solid mode converges towards the purely hydrodynamic one, whereas the synchronous mode becomes marginally unstable in our analysis not converging to the purely hydrodynamic analysis where it is never destabilised.

Wind turbine developments have led to more powerful offshore rotor systems, creating complex aero-hydro-servo-elastic behaviors that require numerical analysis. A mutliphysics problem can be modelled using several approaches: a “monolithic” method where the systems are considered as a unique block or a “partitioned coupling” where the different domains are solved sequentially. The latter is the retained technique for this work in which different solvers are related to distinct equations that require independent time discretisations. The focus is set on coupling a wind turbine’s mechanical solver with an aerodynamic code, the latter being modelled through an inviscid vortex method and the structural aspect using a finite element method. The study aims to present the implementation process and comparison of different time integration coupling schemes within a large wind turbine simulation framework where aeroelastic effects are studied on the IEA 15MW wind turbine. A ”Conventional Serial Staggered” (CSS) scheme is used as a reference coupling technique, allowing independent time integration while limiting coupling to a single time step. Alternatively, a resembling “subcycling” architecture is proposed and implemented to remedy cases with different temporal discretisations and reduce computational costs of CSS when using the inviscid vortex method.

Biofilms are spatially organized communities of microorganisms embedded in a self-produced organic matrix, conferring to the population emerging properties such as an increased tolerance to the action of antimicrobials. It was shown that some bacilli were able to swim in the exogenous matrix of pathogenic biofilms and to counterbalance these properties. Swimming bacteria can deliver antimicrobial agents in situ, or potentiate the activity of antimicrobial by creating a transient vascularization network in the matrix. Hence, characterizing swimmer trajectories in the biofilm matrix is of particular interest to understand and optimize this new biocontrol strategy in particular, but also more generally to decipher ecological drivers of population spatial structure in natural biofilms ecosystems. In this study, a new methodology is developed to analyze time-lapse confocal laser scanning images to describe and compare the swimming trajectories of bacilli swimmers populations and their adaptations to the biofilm structure. The method is based on the inference of a kinetic model of swimmer populations including mechanistic interactions with the host biofilm. After validation on synthetic data, the methodology is implemented on images of three different species of motile bacillus species swimming in a Staphylococcus aureus biofilm. The fitted model allows to stratify the swimmer populations by their swimming behavior and provides insights into the mechanisms deployed by the micro-swimmers to adapt their swimming traits to the biofilm matrix.

An analysis of calibration for reduced-order models (ROMs) is presented in this work. The Galerkin and least-squares Petrov-Galerkin (LSPG) methods are tested on compressible flows involving a disparity of temporal scales. A novel calibration strategy is proposed for the LSPG method and two test cases are analyzed. The first consists of a subsonic airfoil flow where boundary layer instabilities are responsible for trailing-edge noise generation and the second comprises a supersonic airfoil flow with a transient period where a detached shock wave propagates upstream at the same time that shock-vortex interaction occurs at the trailing edge. Results show that calibration produces stable and long-time accurate for both cases. In order to reduce the computational costs of the LSPG models, an accelerated greedy missing point estimation (MPE) algorithm is employed for hyper-reduction. For the first case investigated, LSPG solutions obtained with hyper-reduction show good comparison with those obtained by the full order model. However, for the supersonic case the transient features of the flow need to be properly captured by the sampled points. Otherwise, the dynamics of the moving shock wave are not fully recovered. The impact of different time-marching schemes is also assessed and, differently than reported in literature, Galerkin models are shown to be more accurate than those computed by LSPG when the non-conservative form of the Navier-Stokes equations are solved. For the supersonic case, the Galerkin and LSPG models (without hyper-reduction) capture the overall dynamics of the detached and oblique shock waves along the airfoil. However, when shock-vortex interaction occurs at the trailing-edge, the Galerkin ROM is able to capture the high-frequency fluctuations from vortex shedding while the LSPG presents a more dissipative solution, not being able to recover the flow dynamics.

We investigate the role of linear mechanisms in the emergence of nonlinear horizontal self-propelled states of a heaving foil in a quiescent fluid. Two states are analyzed: a periodic state of unidirectional motion and a quasi-periodic state of slow back & forth motion around a mean horizontal position. The states emergence is explained through a fluid-solid Floquet stability analysis of the non-propulsive symmetric base solution. Unlike a purely-hydrodynamic analysis, our analysis accurately determine the locomotion states onset. An unstable synchronous mode is found when the unidirectional propulsive solution is observed. The obtained mode has a propulsive character, featuring a mean horizontal velocity and an asymmetric flow that generates a horizontal force accelerating the foil. An unstable asynchronous mode, also featuring flow asymmetry and a non-zero velocity, is found when the back & forth state is observed. Its associated complex multiplier introduces a slow modulation of the flapping period, agreeing with the quasi-periodic nature of the back & forth regime. The temporal evolution of this perturbation shows how the horizontal force exerted by the flow is alternatively propulsive or resistive over a slow period. For both modes, an analysis of the velocity and force perturbation time-averaged over the flapping period is used to establish physical instability criteria. The behaviour for large solid-to-fluid density ratio of the modes is thus analyzed. The asynchronous fluid-solid mode converges towards the purely-hydrodynamic one, whereas the synchronous mode becomes marginally unstable in our analysis not converging to the purely-hydrodynamic analysis where it is never destabilised.

We propose a projection-based model order reduction procedure for the ageing of large prestressed concrete structures. Our work is motivated by applications in the nuclear industry, particularly in the simulation of containment buildings. Such numerical simulations involve a multi-modeling approach: a three-dimensional nonlinear thermo-hydro-visco-elastic rheological model is used for concrete; and prestressing cables are described by a one-dimensional linear thermo-elastic behavior. A kinematic linkage is performed in order to connect the concrete nodes and the steel nodes: coincident points in each material are assumed to have the same displacement. We develop an adaptive algorithm based on a Proper Orthogonal Decomposition (POD) in time and greedy in parameter to build a reduced order model (ROM). The nonlinearity of the operator entails that the computational cost of the ROM assembly scales with the size of the high-fidelity model. We develop an hyper-reduction strategy based on empirical quadrature to bypass this computational bottleneck: our approach relies on the construction of a reduced mesh to speed up online assembly costs of the ROM. We provide numerical results for a standard section of a double-walled containment building using a qualified and broadly-used industrial grade finite element solver for structural mechanics (code\\(\\_\\)aster).

We propose a projection-based model order reduction procedure for a general class of parametric quasi-static problems in nonlinear mechanics with internal variables. The methodology is integrated in the industrial finite element code code aster. Model order reduction aims to lower the computational cost of engineering studies that involve the simulation to a costly high-fidelity differential model for many different parameters, which correspond, for example to material properties or initial and boundary conditions. We develop an adaptive algorithm based on a POD-Greedy strategy, and we develop an hyper-reduction strategy based on an element-wise empirical quadrature in order to speed up the assembly costs of the reduced-order model by building an appropriate reduced mesh. We introduce a cost-efficient error indicator which relies on the reconstruction of the stress field by a Gappy-POD strategy. We present numerical results for a three-dimensional elastoplastic system in order to illustrate and validate the methodology.