Clustering and flow around a sphere moving into a grain cloud

International audienc

Clustering and flow around a sphere moving into a grain cloud

International audienc

Computing optimal Strokes for Low Reynolds Number Swimmers

We discuss connections between low-Reynolds-number swimming and geometric control theory, and present a general algorithm for the numerical computation of energetically optimal strokes. As an illustration of our approach, we show computed motility maps and optimal strokes for two model swimmers

Application of the Sparse Cardinal Sine Decomposition to 3D Stokes Flows

International audienceIn boundary element method (BEM), one encounters linear system with a dense and non-symmetric square matrix which might be so large that inverting the linear system is too prohibitive in terms of cpu time and/or memory. Each usual powerful treatment (Fast Multipole Method, H-matrices) developed to deal with this issue is optimized to efficiently perform matrix vector products. This work presents a new technique to adequately and quickly handle such products: the Sparse Cardinal Sine Decomposition. This approach, recently pioneered for the Laplace and Helmholtz equations, rests on the decomposition of each encountered kernel as series of radial Cardinal Sine functions. Here, we achieve this decomposition for the Stokes problem and implement it in MyBEM, a new fast solver for multi-physical BEM. The reported computational examples permit us to compare the advocated method against a usual BEM in terms of both accuracy and convergence

An Optimization-Based Discrete Element Model for Dry Granular Flows: Application to Granular Collapse on Erodible Beds

Erosion processes and the associated static/flowing transition in granular flows are still poorly understood despite their crucial role in natural hazards such as landslides and debris flows. Continuum models do not yet adequately reproduce the observed increase of runout distance of granular flows on erodible beds or the development of waves at the bed/flow interface. Discrete Element Methods, which simulate each grain’s motion and their complex interactions, provide a unique tool to investigate these processes numerically. Among them, Convex Methods (CM), resulting from the convexification of Contact Dynamics methods, benefit from a robust theoretical framework, ensuring the convergence of the numerical solution at every time iteration. They are also intrinsically more stable than classical Molecular Dynamics methods. However, although already implemented in engineering fields, CMs have not yet been tested in the framework of flows on erodible beds. We present here a Convex Optimization Contact Dynamics (COCD) method and prove that it generates a numerical solution verifying Coulomb’s law at each contact and iteration. After its calibration and validation with experiments and another widely used Contact Dynamics method, we show that our simulations accurately reproduce qualitative and even many quantitative characteristics of experimental granular flows on erodible beds, including the increase of runout distance with the thickness of the erodible bed, the spatio-temporal change of the static/flowing interface and the presence of erosion waves behind the flow front. Beyond erosion processes, our study endorses CMs as potential accurate tools for exploring complex granular mechanisms

Ultrasound-induced dense granular flows: a two-time scale modeling

Understanding the mechanisms behind the remote triggering of landslides by seismic waves at micro-strain amplitude is essential for quantifying seismic hazards. Granular materials provide a relevant model system to investigate landslides within the unjamming transition framework, from solid to liquid states. Furthermore, recent laboratory experiments have revealed that ultrasound-induced granular avalanches can be related to a reduction in theinterparticle friction through shear acoustic lubrication of contacts. However, investigating slip at the scale of grain contacts within an optically opaque granular medium remains a challenging issue. Here, we propose an original coupling model and numerically investigate 2D dense granular flows triggered by basal acoustic waves. We model the triggering dynamics at two separated time-scales—one for grain motion (milliseconds) and the other for ultrasound (10 microseconds)—relying the computation of vibrational modes with a discrete element method through the reduction of the local friction. We show that ultrasound predominantly propagates through the strong-force chains, while the ultrasound-induced decrease of interparticle friction occurs in the weak contact forces perpendicular to the strong-force chains. This interparticle-friction reduction initiates local rearrangements at the grain scale that eventually lead to a continuous flow through a percolation process at the macroscopic scale—with a delay depending the proximity to the failure. Consitent with theexperiment, we show that ultrasound-induced flow appears more uniform in space than pure gravity-driven flow, indicating the role of an effective temperature by ultrasonic vibration

Numerical simulations of granular dam break: comparison between discrete element, Navier-Stokes and thin-layer models

International audienceGranular flows occur in various contexts including laboratory experiments, industrial processes and natural geophysical flows. In order to investigate their dynamics, different kinds of physically-based models have been developed. These models can be characterized by the length scale at which dynamic processes are described. Discrete models use a microscopic scale to model individually each grain, Navier-Stokes models use a mesoscopic scale to consider elementary volumes of grains, and thin-layer models use a macroscopic scale to model the dynamics of elementary columns of fluids. In each case, the derivation of the associated equations is well known. However, few studies focus on the extent to which these modeling solutions yield mutually coherent results. In this work, we compare the simulations of a granular dam break on a horizontal or inclined plane, for the discrete model COCD, the Navier-Stokes model Basilisk, and the thin-layer model SHALTOP. We show that, although all three models allow reproducing the temporal evolution of the free surface in the horizontal case (except for SHALTOP at the initiation), the modeled flow dynamics are significantly different, and in particular during the stopping phase. The pressures measured at the flow's bottom are in relatively good agreement, but significant variations are obtained with the COCD model due to complex and fast-varying granular lattices. Similar conclusions are drawn using the same rheological parameters to model a dam break on an inclined plane. This comparison exercise is essential for assessing the limits and uncertainties of granular flow modeling

Optimally swimming stokesian robots

We study self-propelled stokesian robots composed of assemblies of balls, in dimensions 2 and 3, and prove that they are able to control their position and orientation. This is a result of controllabthty, and its proof relies on applying Chow's theorem in an analytic framework, similar to what has been done in [4] for an axisymmetric system swimming along the axis of symmetry. We generalize the analyticity result given in [4] to the situation where the swimmers can move either in a plane or in three-dimensional space, hence experiencing also rotations. We then focus our attention on energetically optimal strokes, which we are able to compute numerically. Some examples of computed optimal strokes are discussed in detail