arXiv subjects

Gabriel D. Weymouth

Publications and source records attributed to Gabriel D. Weymouth.

At least 19 recordsLinked to original sources

arXiv2026

Scaling WaterLily.jl with MPI and an improved geometric multigrid solver

We present recent performance-oriented developments in WaterLily, a scale-resolving incompressible flow solver written in pure Julia that runs seamlessly on CPUs and GPUs of any vendor. Supported by the newly added MPI-based parallelism, strong-scalability tests display a near-ideal linear trend, and weak-scaling efficiency is kept above 85% before node memory-concurrency contention dominates parallel performance. Inter-node weak scalability is sustained above 96% with grid size up to 1 billion cells. We further benchmark improvements to the geometric multigrid Poisson solver enabled by an adaptive under-relaxed red-black Gauss-Seidel smoother together with anisotropic coarsening operators.

physics.comp-ph↗

arXiv2026

Stability of Kirigami parachutes in effectively infinite numerical domains

Kirigami, the art of cutting flat sheets into deployable 3D structures, has recently inspired a new class of parachutes which can deploy into a naturally stable inverted canopy. However, the dynamic mechanism, fluid forces, and geometrical parameters that grant this stability have not yet been clearly identified. In this paper, we use a novel Biot-Savart far-field boundary condition to perform prescribed acceleration and free-falling simulations in effectively infinite domains, tracking the descent of a parameterized kirigami parachute. The far-field velocity is reconstructed from the interior vorticity, resulting in less than 0.1% variation in the predicted dynamics as the domain size is doubled. We first show the linear forces drop 2-5 times as the parachute is deployed due to increased permeability, whereas the moments increase due the counterbalancing effect of the increased lever-arm. Next, we find that the kirigami parachute achieves stable flight for deployment heights as small as half its radius, quickly damping out applied perturbations. For smaller deployments, the parachute tumbles due to side-slip and rotational coupling, as in falling disks. These effectively unbounded simulations identify that deployments approximately equal to the radius offer high drag forces with strong dynamic stability, providing a simple design rule for deployable parachutes.

physics.flu-dyn↗

arXiv2026

Sharp-interface Simulations of Energetic Multiphase Flows with Large Density and Viscosity Ratios

Flows with high density ratios, such as wave breaking and air entrainment in maritime applications, remain challenging to simulate due to their energetic and strongly nonlinear nature. In such regimes, maintaining numerical robustness is difficult when using the commonly adopted velocity-based formulation. The Consistent Mass-Momentum (CMOM) transport framework improves numerical robustness by enforcing fundamental physical properties, most notably momentum conservation and semi-discrete energy-conserving. However, CMOM replaces the advection of a continuous velocity field with that of a discontinuous momentum field. When combined with sharp interface methods, this leads to severe momentum shocks, for which conventional shock-capturing schemes are ineffective. To reconcile physical fidelity with numerical robustness, this work proposes a Synchronized Donor-Region of Momentum fluxes (SynDRoM) that enforces monotonicity of the transported velocity field. The resulting algorithm effectively eliminates spurious velocity oscillations without sacrificing physical fidelity, as demonstrated through scalar transport and interfacial shear instability test cases. Beyond difficulties from large density ratio, improper estimation of viscosity in the vicinity of the interface can introduce numerical instabilities at finite time steps, thereby undermining overall robustness. To address this issue, a viscosity limiter based on the bounded kinetic viscosity concept is introduced and validated using a gravity-driven plane shear flow. Finally, a breaking wave simulation is performed to assess the combined performance of the proposed physics-preserving numerical schemes for multiphase flows.

physics.flu-dyn↗

arXiv2025

Boundary layer flow dynamics of propulsive flapping foils with increasing Reynolds numbers

We study flapping foils at optimally propulsive Strouhal number $St=0.3$ with increasing chord-based Reynolds number at $Re = 10^4$, $10^5$, and $10^6$ to examine changes in their unsteady boundary layers. Despite being prescribed the same freestream, the inner boundary layer characteristics exhibit different trends due to the generation of leading-edge vortices (LEVs) and their advection into the downstream flow. Propulsive flapping foils show an extended laminar region known as the relaminarization, during which the velocity profiles deviate from the standard log law. This relaminarization is accompanied by a significant decrease in the cyclic fluctuation of the wall friction coefficient and an increase in the shape factor while the freestream velocity increases under favourable pressure gradient conditions. This phenomenon intensifies with increasing $Re$. We found that higher $Re$ produces smaller LEVs in greater quantities, with a more rapid but stable breakdown, without resulting in a more chaotic turbulent downstream. This study strongly indicates that the relaminarization could extend beyond $Re=10^6$ as predicted by Fukagata[Annual Review of Fluid Mechanics, 2023]. The results support the potential for further exploration of flapping foils at high $Re$ for noise and drag reduction.

physics.flu-dyn↗

arXiv2025

WaterLily.jl: A differentiable and backend-agnostic Julia solver for incompressible viscous flow around dynamic bodies

Integrating computational fluid dynamics (CFD) solvers into optimization and machine-learning frameworks is hampered by the rigidity of classic computational languages and the slow performance of more flexible high-level languages. In this work, we introduce WaterLily.jl: an open-source incompressible viscous flow solver written in the Julia language. An immersed boundary method is used to enforce the effect of solid boundaries on flow past complex geometries with arbitrary motions. The small code base is multidimensional, multiplatform and backend-agnostic, ie. it supports serial and multithreaded CPU execution, and GPUs of different vendors. Additionally, the pure-Julia implementation allows the solver to be fully differentiable using automatic differentiation. The computational cost per time step and grid point remains constant with increasing grid size on CPU backends, and we measure up to two orders of magnitude speed-up on a supercomputer GPU compared to serial CPU execution. This leads to comparable performance with low-level CFD solvers written in C and Fortran on research-scale problems, opening up exciting possible future applications on the cutting edge of machine-learning research.

physics.flu-dyn↗

arXiv2025

Predicting airfoil pressure distribution using boundary graph neural networks

Surrogate models are essential for fast and accurate surface pressure and friction predictions during design optimization of complex lifting surfaces. This study focuses on predicting pressure distribution over two-dimensional airfoils using graph neural networks (GNNs), leveraging their ability to process non-parametric geometries. We introduce boundary graph neural networks (B-GNNs) that operate exclusively on surface meshes and compare these to previous work on volumetric GNNs operating on volume meshes. All of the training and evaluation is done using the airfRANS (Reynolds-averaged Navier-Stokes) database. We demonstrate the importance of all-to-all communication in GNNs to enforce the global incompressible flow constraint and ensure accurate predictions. We show that supplying the B-GNNs with local physics-based input-features, such as an approximate local Reynolds number $\mathrm{Re}_x$ and the inviscid pressure distribution from a panel method code, enables a $83\%$ reduction of model size and $87\%$ of training set size relative to models using purely geometric inputs to achieve the same in-distribution prediction accuracy. We investigate the generalization capabilities of the B-GNNs to out-of-distribution predictions on the S809/27 wind turbine blade section and find that incorporating inviscid pressure distribution as a feature reduces error by up to $88\%$ relative to purely geometry-based inputs. Finally, we find that the physics-based model reduces error by $85\%$ compared to the state-of-the-art volumetric model INFINITY.

physics.flu-dyn↗

arXiv2025

Using Biot-Savart boundary conditions for unbounded external flow on Eulerian meshes

We introduce a novel boundary condition for incompressible Eulerian simulations formulated using a Biot-Savart vorticity integral that maintains high-accuracy results even when the domain boundary is within a body-length of immersed solid boundaries. The key prerequisite to accurately couple the Biot-Savart condition to the Eulerian velocity and pressure fields is including the influence of the vorticity generated at the immersed boundaries during the incompressible-flow projection step. While the resulting linear operator for the pressure is non-local, it can be efficiently solved by partitioning it into the standard local Poisson operator and the Biot-Savart update. We use oct-tree clustering for the Fast Multi-level Method (FM$\ell$M) to reduce the computational cost of the evaluation of the Biot-Savart integral on the boundaries of a 3D simulation with $N$ points from $O(N^{5/3})$ to $O(N)$ and show that this has bounded errors. We show that the new method captures the analytical added-mass force of accelerating 2D and 3D plates exactly and matches experimentally measured wake development even when the entire domain only extends 1/2 diameter from the plate. The new method also predicts accurate time-varying forces for a 2D circle and 3D sphere regardless of domain size, while classical boundary conditions require a domain more than 100 times larger in 2D to converge on the new method's result. Finally, we study the highly sensitive 2D deflected wakes produced by high frequency flapping foils to the new boundary conditions and show that truncating the deflected wake within four cord-lengths of the body changes the body force amplitudes by 10-40%. Doubling the wake size recovers the asymptotic results to within 5%.

physics.flu-dyn↗

arXiv2024

Closed-loop underwater soft robotic foil shape control using flexible e-skin

The use of soft robotics for real-world underwater applications is limited, even more than in terrestrial applications, by the ability to accurately measure and control the deformation of the soft materials in real time without the need for feedback from an external sensor. Real-time underwater shape estimation would allow for accurate closed-loop control of soft propulsors, enabling high-performance swimming and manoeuvring. We propose and demonstrate a method for closed-loop underwater soft robotic foil control based on a flexible capacitive e-skin and machine learning which does not necessitate feedback from an external sensor. The underwater e-skin is applied to a highly flexible foil undergoing deformations from 2% to 9% of its camber by means of soft hydraulic actuators. Accurate set point regulation of the camber is successfully tracked during sinusoidal and triangle actuation routines with an amplitude of 5% peak-to-peak and 10-second period with a normalised RMS error of 0.11, and 2% peak-to-peak amplitude with a period of 5 seconds with a normalised RMS error of 0.03. The tail tip deflection can be measured across a 30 mm (0.15 chords) range. These results pave the way for using e-skin technology for underwater soft robotic closed-loop control applications.

cs.RO↗

arXiv2024

Resolvent analysis of a swimming foil

This study employs resolvent analysis to explore the dynamics and coherent structures in the boundary layer of a foil that swims via a travelling wave undulation. A modified NACA foil shape is used together with undulatory kinematics to represent fish-like bodies at realistic Reynolds numbers ($ \mathit{Re} = 10,000 $ and $ \mathit{Re} = 100,000 $) in both thrust- and drag-producing propulsion regimes. We introduce a novel coordinate transformation that enables the implementation of the data-driven resolvent analysis \citep{herrmann_data-driven_2021} to dissect the stability of the boundary layer of the swimming foil. This is the first study to implement resolvent analysis on deforming bodies with non-zero thickness and at realistic swimming Reynolds numbers. The analysis reinforces the notion that swimming kinematics drive the system's physics. In drag-producing regimes, it reveals breakdown mechanisms of the propulsive wave, while thrust-producing regimes show a uniform wave amplification across the foil's back half. The key thrust and drag mechanisms scale with the boundary-layer thickness, implying geometric self-similarity in this $\mathit{Re}$ regime. In addition, we identify a mechanism that is less strongly coupled to the body motion. We offer a comparison to a rough foil that reduces the amplification of this mechanism, demonstrating the potential of roughness to control the amplification of key mechanisms in the flow. The results provide valuable insights into the dynamics of swimming bodies and highlight avenues for developing opposition control strategies.

physics.flu-dyn↗

arXiv2023

Immersed-Boundary Fluid-Structure Interaction of Membranes and Shells

This paper presents a general and robust method for the fluid-structure interaction of membranes and shells undergoing large displacement and large added-mass effects by coupling an immersed-boundary method with a shell finite-element model. The immersed boundary method can accurately simulate the fluid velocity and pressure induced by dynamic bodies undergoing large displacements using a computationally efficient pressure projection finite volume solver. The structural solver can be applied to bending and membrane-related problems, making our partitioned solver very general. We use a strongly-coupled algorithm that avoids the expensive computation of the inverse Jacobian within the root-finding iterations by constructing it from input-output pairs of the coupling variables from the previous time steps. Using two examples with large deformations and added mass contributions, we demonstrate that the resulting quasi-Newton scheme is stable, accurate, and computationally efficient.

physics.flu-dyn↗

arXiv2023

WaterLily.jl: A differentiable fluid simulator in Julia with fast heterogeneous execution

Integrating computational fluid dynamics (CFD) software into optimization and machine-learning frameworks is hampered by the rigidity of classic computational languages and the slow performance of more flexible high-level languages. WaterLily.jl is an open-source incompressible viscous flow solver written in the Julia language. The small code base is multi-dimensional, multi-platform and backend-agnostic (serial CPU, multi-threaded, & GPU execution). The simulator is differentiable and uses automatic-differentiation internally to immerse solid geometries and optimize the pressure solver. The computational time per time step scales linearly with the number of degrees of freedom on CPUs, and we see up to a 182x speed-up using CUDA kernels. This leads to comparable performance with Fortran solvers on many research-scale problems opening up exciting possible future applications on the cutting edge of machine-learning research.

physics.flu-dyn↗

arXiv2023

Effects of surface roughness on the propulsive performance of pitching foils

The hydrodynamic influence of surface texture on static surfaces ranges from large drag penalties (roughness) to potential performance benefits (shark-like skin). Although, it is of wide-ranging research interest, the impact of roughness on flapping systems has received limited attention. In this work, we explore the effect of roughness on unsteady performance of a harmonically pitching foil through experiments using foils with different surface roughness, at a fixed Strouhal number and within the Reynolds number (Re) range of 15k-30k. The foils' surface roughness is altered by changing the distribution of spherical-cap shaped elements over the propulsor area. We find that the addition of surface roughness does not improve the performance compared to a smooth surface over the Re range considered. The analysis of the flow fields shows near identical wakes regardless of the foil's surface roughness. The performance reduction mainly occurs due to an increase in profile drag. However, we find that the drag penalty due to roughness is reduced from 76% for a static foil to 16% for a flapping foil at the same mean angle of attack, with the strongest decrease measured at the highest Re. Our findings highlight that the effect of roughness on dynamic systems is very different than that on static systems, thereby, cannot be accounted for by only using information obtained from static cases. This also indicates that the performance of unsteady, flapping systems is more robust to the changes in surface roughness.

physics.flu-dyn↗

arXiv2022

Energy-efficient tunable-stiffness soft robots using second moment of area actuation

The optimal stiffness for soft swimming robots depends on swimming speed, which means no single stiffness can maximise efficiency in all swimming conditions. Tunable stiffness would produce an increased range of high-efficiency swimming speeds for robots with flexible propulsors and enable soft control surfaces for steering underwater vehicles. We propose and demonstrate a method for tunable soft robotic stiffness using inflatable rubber tubes to stiffen a silicone foil through pressure and second moment of area change. We achieved double the effective stiffness of the system for an input pressure change from 0 to 0.8 bar and 2 J energy input. We achieved a resonant amplitude gain of 5 to 7 times the input amplitude and tripled the high-gain frequency range comparedto a foil with fixed stiffness. These results show that changing second moment of area is an energy effective approach tot unable-stiffness robots.

cs.RO↗

arXiv2021

Immersed Boundary Simulations of Flows Driven by Moving Thin Membranes

Immersed boundary methods are extensively used for simulations of dynamic solid objects interacting with fluids due to their computational efficiency and modelling flexibility compared to body-fitted grid methods. However, thin geometries, such as shells and membranes, cause a violation of the boundary conditions across the surface for many immersed boundary projection algorithms. Using a one-dimensional analytical derivation and multi-dimensional numerical simulations, this manuscript shows that adjustment of the Poisson matrix itself is require to avoid large velocity, pressure, and force prediction errors when the pressure jump across the interface is substantial and that these errors increase with Reynolds number. A new minimal thickness modification is developed for the Boundary Data Immersion Method (BDIM-σ),which avoids these issues while still enabling the use of efficient projection algorithms for high-speed immersed surface simulations.

physics.flu-dyn↗

arXiv2021

Deep learning of the spanwise-averaged Navier-Stokes equations

Simulations of turbulent fluid flow around long cylindrical structures are computationally expensive because of the vast range of length scales, requiring simplifications such as dimensional reduction. Current dimensionality reduction techniques such as strip-theory and depth-averaged methods do not take into account the natural flow dissipation mechanism inherent in the small-scale three-dimensional (3-D) vortical structures. We propose a novel flow decomposition based on a local spanwise average of the flow, yielding the spanwise-averaged Navier-Stokes (SANS) equations. The SANS equations include closure terms accounting for the 3-D effects otherwise not considered in 2-D formulations. A supervised machine-learning (ML) model based on a deep convolutional neural network provides closure to the SANS system. A-priori results show up to 92% correlation between target and predicted closure terms; more than an order of magnitude better than the eddy viscosity model correlation. The trained ML model is also assessed for different Reynolds regimes and body shapes to the training case where, despite some discrepancies in the shear-layer region, high correlation values are still observed. The new SANS equations and ML closure model are also used for a-posteriori prediction. While we find evidence of known stability issues with long time ML predictions for dynamical systems, the closed SANS simulations are still capable of predicting wake metrics and induced forces with errors from 1-10%. This results in approximately an order of magnitude improvement over standard 2-D simulations while reducing the computational cost of 3-D simulations by 99.5%.

physics.flu-dyn↗

arXiv2020

Span effect on the turbulence nature of flow past a circular cylinder

Turbulent flow evolution and energy cascades are significantly different in two-dimensional (2D) and three-dimensional (3D) flows. Studies have investigated these differences in obstacle-free turbulent flows, but solid boundaries have an important impact on the cross-over between 3D to 2D turbulence dynamics. In this work, we investigate the span effect on the turbulence nature of flow past a circular cylinder at Re=10000. It is found that even for highly anisotropic geometries, 3D small-scale structures detach from the walls. Additionally, the natural large-scale rotation of the Kármán vortices rapidly two-dimensionalises those structures if the span is 50% of the diameter or less. We show this is linked to the span being shorter than the Mode B instability wavelength. The conflicting 3D small-scale structures and 2D Kármán vortices result in 2D and 3D turbulence dynamics which can coexist at certain locations of the wake depending on the domain geometric anisotropy.

physics.flu-dyn↗

arXiv2015

Lily Pad: Towards Real-time Interactive Computational Fluid Dynamics

Despite the fact that computational fluid dynamics (CFD) software is now (relatively) fast and freely available, it is still amazingly difficult to use. Inaccessible software imposes a significant entry barrier on students and junior engineers, and even senior researchers spend less time developing insights and more time on software issues. Lily Pad was developed as an initial attempt to address some of these problems. The goal of Lily Pad is to lower the barrier to CFD by adopting simple high-speed methods, utilising modern programming features and environments, and giving immediate visual feed-back to the user. The resulting software focuses on the fluid dynamics instead of the computation, making it useful for both education and research. LilyPad is open source and available online at https://github.com/weymouth/lily-pad for all use under the MIT license.

physics.comp-ph↗

arXiv2014

The Numerical Simulation of Ship Waves Using Cartesian-Grid and Volume-of-Fluid Methods

Cartesian-grid methods in combination with immersed-body and volume-of-fluid methods are ideally suited for simulating breaking waves around ships. A surface panelization of the ship hull is used as input to impose body-boundary conditions on a three-dimensional cartesian grid. The volume-of-fluid portion of the numerical algorithm is used to capture the free-surface interface, including the breaking of waves. The numerical scheme is implemented on a parallel computer. Various numerical issues are discussed, including implementing exit boundary conditions, conserving mass using a novel regridding algorithm, improving resolution through the use of stretched grids, minimizing initial transients, and enforcing hull boundary conditions on cartesian grids. Numerical predictions are compared to experimental measurements of ship models moving with forward speed, including model 5415 and model 5365 (Athena). The ability to model forced-motions is illustrated using a heaving sphere moving with forward speed.

physics.flu-dyn↗