Wim M. van Rees

Simulations of single and multiple swimmers with non-divergence free deforming geometries

We present a vortex particle method coupled with a penalization technique to simulate single and multiple swimmers in an incompressible, viscous flow in two and three dimensions. The proposed algorithm can handle arbitrarily deforming bodies and their corresponding non-divergence free deformation velocity fields. The method is validated on a number of benchmark problems with stationary and moving boundaries. Results include flows of tumbling objects and single and multiple self-propelled swimmers.

MRAG-I2D: Multi-resolution adapted grids for remeshed vortex methods on multicore architectures

We present MRAG-I2D,1 an open source software framework, for multiresolution simulations of two-dimensional, incompressible, viscous flows on multicore architectures. The spatiotemporal scales of the flow field are captured by remeshed vortex methods enhanced by high order average-interpolating wavelets and local time-stepping. The multiresolution solver of the Poisson equation relies on the development of a novel, tree-based multipole method. MRAG-I2D implements a number of HPC strategies to map efficiently the irregular computational workload of wavelet-adapted grids on multicore nodes. The capabilities of the present software are compared to the current state-of-the-art in terms of accuracy, compression rates and time-to-solution. Benchmarks include the inviscid evolution of an elliptical vortex, flow past an impulsively started cylinder at Re=40–40000 and simulations of self-propelled anguilliform swimmers. The results indicate that the present software has the same or better accuracy than state-of-the-art solvers while it exhibits unprecedented performance in terms of time-to-solution.

Complete measurement of helicity and its dynamics in vortex tubes.

Linking fluids as they twist and writhe Helicity is a measure of cork-screw-like motion described by the amount of twisting, writhing, and linking in a fluid. Total helicity is conserved for ideal fluids, but how helicity changes in real fluids with even tiny amounts of viscosity has been an open question. Scheeler et al. provide a complete measurement of total helicity in a real fluid by using a set of hydrofoils to track linking, twisting, and writhing (see the Perspective by Moffatt). They show that twisting dissipates total helicity, whereas writhing and linking conserve it. This provides a fundamental insight into tornadogenesis, atmospheric flows, and the formation of turbulence. Science, this issue p. 487; see also p. 448 Total helicity in a real fluid is dissipated through twisting motions, whereas linking and writhing keeps helicity conserved. Helicity, a topological measure of the intertwining of vortices in a fluid flow, is a conserved quantity in inviscid fluids but can be dissipated by viscosity in real flows. Despite its relevance across a range of flows, helicity in real fluids remains poorly understood because the entire quantity is challenging to measure. We measured the total helicity of thin-core vortex tubes in water. For helical vortices that are stretched or compressed by a second vortex, we found conservation of total helicity. For an isolated helical vortex, we observed evolution toward and maintenance of a constant helicity state after the dissipation of twist helicity by viscosity. Our results show that helicity can remain constant even in a viscous fluid and provide an improved basis for understanding and manipulating helicity in real flows.

Synchronisation through learning for two self-propelled swimmers

We study the fluid dynamics of two fish-like bodies with synchronised swimming patterns. Our studies are based on two-dimensional simulations of viscous incompressible flows. We distinguish between motion patterns that are externally imposed on the swimmers and self-propelled swimmers that learn manoeuvres to achieve certain goals. Simulations of two rigid bodies executing pre-specified motion indicate that flow-mediated interactions can lead to substantial drag reduction and may even generate thrust intermittently. In turn we examine two self-propelled swimmers arranged in a leader-follower configuration, with a-priori specified body-deformations. We find that the swimming of the leader remains largely unaffected, while the follower experiences either an increase or decrease in swimming speed, depending on the initial conditions. Finally, we consider a follower that synchronises its motion so as to minimise its lateral deviations from the leaders path. The leader employs a steady gait while the follower uses a reinforcement learning algorithm to adapt its swimming-kinematics. We find that swimming in a synchronised tandem can yield up to about 30% reduction in energy expenditure for the follower, in addition to a 20% increase in its swimming-efficiency. The present results indicate that synchronised swimming of two fish can be energetically beneficial.The coordinated motion by multiple swimmers is a fundamental component in fish schooling. The flow field induced by the motion of each self-propelled swimmer implies non-linear hydrodynamic interactions among the members of a group. How do swimmers compensate for such hydrodynamic interactions in coordinated patterns? We provide an answer to this riddle though simulations of two, self-propelled, fish-like bodies that employ a learning algorithm to synchronise their swimming patterns. We distinguish between learned motion patterns and the commonly used a-priori specified movements, that are imposed on the swimmers without feedback from their hydrodynamic interactions. First, we demonstrate that two rigid bodies executing pre-specified motions, with an alternating leader and follower, can result in substantial drag-reduction and intermittent thrust generation. In turn, we study two self-propelled swimmers arranged in a leader-follower configuration, with a-priori specified body-deformations. These two self-propelled swimmers do not sustain their tandem configuration. The follower experiences either an increase or decrease in swimming speed, depending on the initial conditions, while the swimming of the leader remains largely unaffected. This indicates that a-priori specified patterns are not sufficient to sustain synchronised swimming. We then examine a tandem of swimmers where the leader has a steady gait and the follower learns to synchronize its motion, to overcome the forces induced by the leaders vortex wake. The follower employs reinforcement learning to adapt its swimming-kinematics so as to minimize its lateral deviations from the leaders path. Swimming in such a sustained synchronised tandem yields up to [Formula: see text] reduction in energy expenditure for the follower, in addition to a [Formula: see text] increase in its swimming-efficiency. The present results show that two self-propelled swimmers can be synchronised by adapting their motion patterns to compensate for flow-structure interactions. Moreover, swimmers can exploit the vortical structures of their flow field so that synchronised swimming is energetically beneficial.

Vortex tube reconnection at Re = 104

We present simulations of the long-time dynamics of two anti-parallel vortex tubes with and without initial axial flow, at Reynolds number Re = Γ/ν = 104. Simulations were performed in a periodic domain with a remeshed vortex method using 785 × 106 particles. We quantify the vortex dynamics of the primary vortex reconnection that leads to the formation of elliptical rings with axial flow and report for the first time a subsequent collision of these rings. In the absence of initial axial flow, a −5/3 slope of the energy spectrum is observed during the first reconnection of the tubes. The resulting elliptical vortex rings experience a coiling of their vortex lines imparting an axial flow inside their cores. These rings eventually collide, exhibiting a −7/3 slope of the energy spectrum. Studies of vortex reconnection with an initial axial flow exhibit also the −7/3 slope during the initial collision as well as in the subsequent collision of the ensuing elliptical vortex rings. We quantify the detailed vortex...

Growth patterns for shape-shifting elastic bilayers

Significance Many biological forms, such as leaves, flowers, and faces, are shaped by complex growth patterns. How can we prescribe the rules of growth on a simple surface so that it will morph into a flower or a face? Here, we solve this inverse problem of designing the growth patterns for an anisotropically growing elastic bilayer structure and prove that it can be used to achieve any target surface shape from any reference shape. We demonstrate the applicability of this result via the computational design of growth patterns for animal, vegetable, and mineral surfaces—a face, a flower, and a canyon. Our solution provides algorithms for engineering complex functional shapes in tissues, and actuation systems in soft robotics, and elsewhere. Inspired by the differential-growth-driven morphogenesis of leaves, flowers, and other tissues, there is increasing interest in artificial analogs of these shape-shifting thin sheets made of active materials that respond to environmental stimuli such as heat, light, and humidity. But how can we determine the growth patterns to achieve a given shape from another shape? We solve this geometric inverse problem of determining the growth factors and directions (the metric tensors) for a given isotropic elastic bilayer to grow into a target shape by posing and solving an elastic energy minimization problem. A mathematical equivalence between bilayers and curved monolayers simplifies the inverse problem considerably by providing algebraic expressions for the growth metric tensors in terms of those of the final shape. This approach also allows us to prove that we can grow any target surface from any reference surface using orthotropically growing bilayers. We demonstrate this by numerically simulating the growth of a flat sheet into a face, a cylindrical sheet into a flower, and a flat sheet into a complex canyon-like structure.

Self-propulsion of a counter-rotating cylinder pair in a viscous fluid

We study a self-propelling pair of steadily counter-rotating cylinders in simulations of a two-dimensional viscous fluid. We find two strikingly, opposite directions for the motion of the pair that is characterized by its width and rotational Reynolds number. At low Reynolds numbers and large widths, the cylinder pair moves similarly to an inviscid point vortex pair, while at higher Reynolds numbers and smaller widths, the pair moves in the opposite direction through a jet-like propulsion mechanism. Increasing further the Reynolds number, or decreasing the width, gives rise to non-polarised motion governed by the shedding direction and frequency of the boundary-layer vorticity. We discuss the fundamental physical mechanisms for these two types of motion and the transitions in the corresponding phase diagram. We discuss the fluid dynamics of each regime based on streamline plots, tracer particles, and the vorticity field. The counter rotating cylinder pair serves as a prototype for self-propelled bodies and suggests possible engineering devices composed of simple components and tunable by the rotation and width of the cylinder pair.

Mechanics of biomimetic 4D printed structures

Recent progress in additive manufacturing and materials engineering has led to a surge of interest in shape-changing plate and shell-like structures. Such structures are typically printed in a planar configuration and, when exposed to an ambient stimulus such as heat or humidity, swell into a desired three-dimensional geometry. Viewed through the lens of differential geometry and elasticity, the application of the physical stimulus can be understood as a local change in the metric of a two dimensional surface embedded in three dimensions. To relieve the resulting elastic frustration, the structure will generally bend and buckle out-of-plane. Here, we propose a numerical approach to convert the discrete geometry of filament bilayers, associated with print paths of inks with given material properties, into continuous plates with inhomogeneous growth patterns and thicknesses. When subject to prescribed growth anisotropies, we can then follow the evolution of the shapes into their final form. We show that our results provide a good correspondence between experiments and simulations, and lead to a framework for the prediction and design of shape-changing structures.