publications

2026

1. Preprint

   Composite B-spline Current Deposition and Interpolation Operators for Thin-Wire Finite-Difference Time-Domain Simulations

   Cole Gruninger and Boyce E. Griffith

   arXiv preprint arXiv:2605.21450, May 2026

   Abs

   We address parasitic low-frequency currents in thin-wire antenna simulations by introducing composite B-spline regularizations that ensure charge conservation. The proposed current deposition and interpolation operators preserve key mathematical properties through discrete adjoint relationships, yielding orientation-independent impedance values consistent with known characteristics while avoiding unphysical artifacts produced by conventional methods.

2. Composite B-spline Regularized Delta Functions for the Immersed Boundary Method: Divergence-free Interpolation and Gradient-Preserving Force Spreading

   Cole Gruninger and Boyce E. Griffith

   Journal of Computational Physics, Feb 2026

   DOI

2025

1. Local Divergence-Free Immersed Finite Element-Difference Method Using Composite B-splines

   Lianxia Li, Cole Gruninger, Jae H. Lee, and 1 more author

   Advances in Computational Science and Engineering, Apr 2025

   Abs DOI

   In the class of immersed boundary (IB) methods, the choice of the regularized delta function plays a crucial role in transferring information between fluid and solid domains through interpolation and spreading operators. Most prior work using the IB method has used isotropic kernels that do not preserve the divergence-free condition of the velocity field, leading to loss of incompressibility of the solid when interpolating the Eulerian velocity to Lagrangian markers. One approach to addressing this issue in IB simulations involving large deformations of immersed incompressible elastic structures is to use a volumetric stabilization approach, such as adding a volumetric energy term and using modified invariants in the structure’s constitutive model. Composite B-spline (CBS) kernels offer an alternative approach by inherently maintaining the discrete divergence-free property. This work evaluates the performance of CBS kernels in terms of their volume conservation and accuracy, comparing them with several traditional isotropic kernel functions using a construction introduced by Peskin (referred to as IB kernels) and B-spline (BS) kernels. Benchmark tests include pressure-loaded and shear-dominated flows, such as an elastic band under differential pressure loads, a pressurized membrane, a compressed block, Cook’s membrane, a slanted channel flow, and a modified Turek-Hron problem. Additionally, we validate our methodology using a complex fluid-structure interaction model of bioprosthetic heart valve dynamics in a pulse duplicator. Results demonstrate that CBS kernels achieve superior volume conservation compared to conventional isotropic kernels, eliminating the need for additional volumetric stabilization techniques typically required to address instabilities arising from volume conservation errors. Further, it is common that the accuracy provided by CBS kernels on coarser grids is comparable to that provided by IB and BS kernels on finer grids. Unlike IB and BS kernels, which perform better with larger mesh ratio factors between solid and fluid grids, CBS kernels show improved results with smaller mesh ratio factors. Additionally, the study reveals that although wider kernels provide more accurate results across all methods, CBS kernels are less sensitive to variations in relative grid spacings than isotropic kernels. This study highlights the advantages of CBS kernels in achieving stable, accurate, and efficient FSI simulations without requiring specialized volumetric stabilization treatments when simulating large deformations of elastic solids immersed in fluid.

2024

1. Flagellum Pumping Efficiency in Shear-Thinning Viscoelastic Fluids

   Aaron Barrett, Aaron L. Fogelson, M. Gregory Forest, and 3 more authors

   Journal of Fluid Mechanics, Nov 2024

   Abs DOI

   , Microorganism motility often takes place within complex, viscoelastic fluid environments, e.g. sperm in cervicovaginal mucus and bacteria in biofilms. In such complex fluids, strains and stresses generated by the microorganism are stored and relax across a spectrum of length and time scales and the complex fluid can be driven out of its linear response regime. Phenomena not possible in viscous media thereby arise from feedback between the swimmer and the complex fluid, making swimming efficiency co-dependent on the propulsion mechanism and fluid properties. Here, we parameterize a flagellar motor and filament properties together with elastic relaxation and nonlinear shear-thinning properties of the fluid in a computational immersed boundary model. We then explore swimming efficiency, defined as a particular flow rate divided by the torque required to spin the motor, over this parameter space. Our findings indicate that motor efficiency (measured by the volumetric flow rate) can be boosted or degraded by relatively moderate or strong shear thinning of the viscoelastic environment.

2. Benchmarking the Immersed Boundary Method for Viscoelastic Flows

   Cole Gruninger, Aaron Barrett, Fuhui Fang, and 2 more authors

   Journal of Computational Physics, Jun 2024

   Abs DOI

   We present and analyze a series of benchmark tests regarding the application of the immersed boundary (IB) method to viscoelastic flows through and around non-trivial, stationary geometries. The IB method is widely used to simulate biological fluid dynamics and other modeling scenarios in which a structure is immersed in a fluid. Although the IB method has been most commonly used to model systems involving viscous incompressible fluids, it also can be applied to visoelastic fluids and has enabled the study of a wide variety of dynamical problems including the settling of vesicles and the swimming of elastic filaments in fluids modeled by the Oldroyd-B constitutive equation. In the viscoelastic context, however, relatively little work has explored the accuracy or convergence properties of this numerical scheme. Herein, we present benchmarking results for an IB solver applied to viscoelastic flows in and around non-trivial geometries using either the idealized Oldroyd-B constitutive model or the more physically realistic, polymer-entanglement-based Rolie-Poly constitutive equations. We use two-dimensional numerical test cases along with results from rheology experiments to benchmark the IB method and compare it to more complex finite element and finite volume viscoelastic flow solvers. Additionally, we analyze different choices of regularized delta function and relative Lagrangian grid spacings which allow us to identify and recommend the key choices of these numerical parameters depending on the present flow regime.

2023

1. Visible Light Induced Formation of a Tungsten Hydride Complex

   Diane P. Isaacs, Cole T. Gruninger, Tao Huang, and 5 more authors

   Dalton Transactions, Mar 2023

   Abs DOI

   When irradiated with blue light in the presence of a Lewis base (L), [CpW(CO)3]2 undergoes metal–metal bond cleavage followed by a disproportionation reaction to form [CpW(CO)3L]+ and [CpW(CO)3]-. Here, we show that in the presence of pyridinium tetrafluoroborate, [CpW(CO)3]- reacts further to form a metal hydride complex CpW(CO)3H. The rection was monitored through in situ photo 1H NMR spectroscopy experiments and the mechanism of light-driven hydride formation was investigated by determining quantum yields of formation. Quantum yields of formation of CpW(CO)3H correlate with I-1/2 (I = photon flux on our sample tube), indicating that the net disproportionation of [CpW(CO)3]2 to form the hydride precursor [CpW(CO)3]- occurs primarily through a radical chain mechanism.

2020

1. Electrosynthetic Route to Cyclopentadienyl Rhenium Hydride Complexes Enabled by Electrochemical Investigations of Their Redox-Induced Formation

   Tao Huang, Tayliz M. Rodriguez, Cole T. Gruninger, and 4 more authors

   Organometallics, May 2020

   Abs DOI

   As the utility of electroanalytical methods to study reaction mechanisms continues to develop, a wider scope of chemical reactions will fall under the scrutiny of electrochemical investigation. We report herein thermochemical and electrosynthetic routes to stable rhenium hydride complexes ReClCp(H)(dppx) (dppx = 1,1-bis(diphenylphosphino)methane (dppm), 1,2-bis(diphenylphosphino)ethane (dppe), 1,3-bis(diphenylphosphino)propane (dppp), Cp = cyclopentadienyl). These complexes are accessed via reduction of the corresponding ReCl3(dppx)(PPh3) in the presence of cyclopentadiene, which was initially achieved by a traditional chemical route. Complementary chemical and electrochemical methods were used to elucidate the mechanism by which the rhenium hydride complexes form. Notably, reduction of the Re(III) precursor proceeds via an ECE mechanism, liberating chloride ions that can detrimentally react with unreduced precursor. Further, a pair of key Re(I) intermediates (one with and one without coordinated N2) were isolated and characterized and shown to have dramatic differences in reactivity with CpH. Guided by mechanistic insight, an efficient electrochemical synthesis route was designed through which the rhenium hydride complex is accessed in 96% yield with 90% Faradaic efficiency. While many organometallic complexes have only been accessed with traditional chemical reductants, this work highlights that a detailed mechanistic understanding enables the robust translation of these processes to electrosynthetic reactions.

2. Redox Mediators Accelerate Electrochemically-Driven Solubility Cycling of Molecular Transition Metal Complexes

   Katherine J. Lee, Kunal M. Lodaya, Cole T. Gruninger, and 2 more authors

   Chemical Science, 2020

   DOI
3. Analysis of Multi-Electron, Multi-Step Homogeneous Catalysis by Rotating Disc Electrode Voltammetry: Theory, Application, and Obstacles

   Katherine J. Lee, Cole T. Gruninger, Kunal M. Lodaya, and 3 more authors

   Analyst, Feb 2020

   Abs DOI

   Rotating disc electrode (RDE) voltammetry has been widely adopted for the study of heterogenized molecular electrocatalysts for multi-step fuel-forming reactions but this tool has never been comprehensively applied to their homogeneous analogues. Here, the utility and limitations of RDE techniques for mechanistic and kinetic analysis of homogeneous molecular catalysts that mediate multi-electron, multi-substrate redox transformations are explored. Using the ECEC\prime reaction mechanism as a case study, two theoretical models are derived based on the Nernst diffusion layer model and the Hale transformation. Current–potential curves generated by these computational strategies are compared under a variety of limiting conditions to identify conditions under which the more minimalist Nernst Diffusion Layer approach can be applied. Based on this theoretical treatment, strategies for extracting kinetic information from the plateau current and the foot of the catalytic wave are derived. RDEV is applied to a cobaloxime hydrogen evolution reaction (HER) catalyst under non-aqueous conditions in order to experimentally validate this theoretical framework and explore the feasibility of RDE as a tool for studying homogeneous catalysts. Crucially, analysis of the foot-of-the-wave via this theoretical framework provides rate constants for elementary reaction steps that agree with those extracted from stationary voltammetric methods, supporting the application of RDE to study homogeneous fuel-forming catalysts. Finally, obstacles encountered during the kinetic analysis of cobaloxime, along with the voltammetric signatures used to diagnose this reactivity, are discussed with the goal of guiding groups working to improve RDE set-ups and help researchers avoid misinterpretation of RDE data.