A computational model of aquatic animal locomotion

Numerical Methods for Unconstrained Optimization and Nonlinear Equations

Dennis, J. E., & Schnabel, R. B. (1996) · Society for Industrial and Applied Mathematics eBooks · doi:10.1137/1.9781611971200 · Cited by 7,673

Numerical Solution of the Navier-Stokes Equations

CHORIN, A. J. (1968) · Mathematics of Computation · doi:10.1090/s0025-5718-1968-0242392-2 · Cited by 5,902

Numerical analysis of blood flow in the heart

Peskin, C. S. (1977) · Journal of Computational Physics · doi:10.1016/0021-9991(77)90100-0 · Cited by 3,108

Mathematical Biofluiddynamics

Lighthill, S. J. (1975) · Society for Industrial and Applied Mathematics eBooks · doi:10.1137/1.9781611970517 · Cited by 895

Mechanics of Swimming and Flying

Childress, S. (1981) · Cambridge University Press eBooks · doi:10.1017/cbo9780511569593 · Cited by 417

Mechanics of Swimming and Flying

Craik, A. D. D., & Childress, S. (1982) · Biometrics · doi:10.2307/2530474 · Cited by 389

A note on a swimming problem

Tuck, E. O. (1968) · Journal of Fluid Mechanics · doi:10.1017/s0022112068000169 · Cited by 124

Emergent Kinematics and Flow Structure of Tension Driven Pulsing Xeniid Corals

Santiago, M., Hoover, A., & Miller, L. A. (2025) · Bulletin of Mathematical Biology · doi:10.1007/s11538-025-01493-3 · Cited by 1

A Microscale Model Of Biofilm Formation In Porous Media

Dillon, R. H., Fauci, L., & Meng, D. (1998) · WIT transactions on ecology and the environment · doi:10.2495/cmwr980601 · Cited by 1

Numerical Study on the Dynamics of Organism Motion under Background Flow

Maniyeri, R., & Kang, S. (2017) · International Conference on Bioinformatics and Biomedical Science (ICBBS) · doi:10.1145/3121138.3121169 · Cited by 1

A new SOR-type iteration method for solving linear systems

Liu, K., Yang, J., & Shi, W. (2019) · Applied Mathematics Letters · doi:10.1016/j.aml.2019.106104 · Cited by 1

Simulation of the dynamic flow field in the left ventricle of the heart during diastolic filling

Adu, J., Yin, L., Zhang, H., Xie, S., & Lü, J. (2020) · AIP Advances · doi:10.1063/1.5126470 · Cited by 1

Molecular to Multicellular Deformation during Adhesion of Immune Cells Under Flow

Gee, D. J., & King, M. R. (2010) · doi:10.1002/9780470579831.ch12 · Cited by 1

Viscoelastic flow in a collapsible channel

Chakraborty, D. (2017) · Figshare · doi:10.26180/4635103 · Cited by 1

Étude numérique de la relaxation de capsules confinées par couplage des méthodes Volumes Finis - Éléments Finis via la méthode des frontières immergées IBM : influence de l'inertie et du degré de confinement.

Sarkis, B. (2018) · doi:10.70675/36b41e04z09c1z49c0zbb0czf3afa32c7b0d · Cited by 1

Immersed Methods for Compressible Fluid–Solid Interactions

Wang, X. S. (2013) · doi:10.1002/9781118402955.ch12

Immersed interface methods. Final report

Washington Univ., S., LeVeque, R. J., Adams, L., & Bube, K. (1996) · doi:10.2172/418466

Chapter 7 Computational Nonlinear Models

(2008) · Monograph series on nonlinear science and complexity · doi:10.1016/s1574-6917(07)00207-3

Deterministic vortex methods for the incompressible Navier-Stokes equations

Russo, G. (2008) · Springer eBooks · doi:10.1007/3-540-54960-9_63

A Weak Formulation of the Immersed Boundary Method

Givelberg, E. (2012) · SIAM Journal on Scientific Computing · doi:10.1137/100785181

ESTIMATION OF THE IMMERSED BOUNDARY TECHNIQUE FOR INDUSTRIAL FLUID DYNAMIC

Marani, P. (2012)

SIMULATION OF THE DYNAMICS OF AN ELASTIC MEMBRANE IN A GROOVED CHANNEL USING A COMBINED LATTICE BOLTZMANN-IMMERSED BOUNDARY METHOD

Alizadeh, A., & Dadvand, A. (2016)

Effect of regularized delta function on accuracy of immersed boundary method

Gong, Z., Lu, C.-J., & Huang, H. (2012) · Applied Mathematics and Mechanics · doi:10.1007/s10483-012-1635-9

Numerical investigation for optimal sensor placement on flapping-wing MAVs

Xu, M., Wei, M., Yang, T., Riddick, J. C., & Hall, A. J. (2013) · AIAA Aerospace Sciences Meeting · doi:10.2514/6.2013-360

MULTI-SCALE COMPUTATION IN HEMODYNAMICS

Abou, N. (2002)

Addressing the Computational Cost of the Immersed Boundary Method through Multi-Implicit and Multi-Rate Strategies with Time Parallelism

Fovargue, L. (2019) · Carolina Digital Repository (University of North Carolina at Chapel Hill) · doi:10.17615/s126-3z52

Chapter 1 Immersed Boundary/Continuum Methods

Wang, X. S. (2010)

Continuous and Discrete Energy Based Methods for Accurate Force Computations on Shells in the Immersed Boundary Method

Maxian, O., Kassen, A., & Strychalski, W. (2017)

Coupled fluid models of smoothed particle hydrodynamics and finite difference method for simulating dynamic penguin huddles

Gu, W. J. (2018)

Wellposedness of a swimming model in the 3-D incompressible fluid governed by the nonstationary Stokes equationPreprint

Khapalov, A. Y. (2012) · arXiv (Cornell University) · doi:10.48550/arxiv.1205.1088

Computational Models for Biological Locomotion in Gels

Alshehri, H. M. (2019)

Pump efficacy in a fluid-structure interaction model of a chain of contracting lymphangionsPreprint

Elich, H., Barrett, A., Shankar, V., & Fogelson, A. L. (2020) · arXiv (Cornell University) · doi:10.48550/arxiv.2012.05377

Numerical simulation of sperm motility under shear flow

Maniyeri, R. (2021) · AIP conference proceedings · doi:10.1063/5.0045739

Local controllability for a “swimming” model.

Khapalov, A. Y. (2007) · IEEE Conference on Decision and Control (CDC) · doi:10.1109/cdc.2007.4435042

Virtual Node Algorithms for Stokes Interface Problems

Assêncio, D. C. (2012) · eScholarship (California Digital Library)

A Numerical Method for Simulating Fast-Swimming Motions

Cortez, R. (2001) · The IMA volumes in mathematics and its applications · doi:10.1007/978-1-4613-0151-6_3

Linearly-Fitted Conservative (Dissipative) Schemes for Nonlinear Wave Equations

Wu, X., & Wang, B. (2021) · Springer eBooks · doi:10.1007/978-981-16-0147-7_8

Study of whirling instability

Liu, W. (2014) · Digital WPI

Enhancement of Active Swimming near Fluid Interfaces

Cartwright, A., & Du, J. Q. (2022) · Journal of Physics Conference Series · doi:10.1088/1742-6596/2224/1/012034

Hazardous materials in aquatic environments of the Mississippi River Basin. Annual technical report, 30 December 1992--29 December 1993

USDOE, W., & Xavier Univ. of Louisiana, N. O. (1993) · OSTI OAI (U.S. Department of Energy Office of Scientific and Technical Information) · doi:10.2172/10145687

References

Boccaletti, S. (2008) · Monograph series on nonlinear science and complexity · doi:10.1016/s1574-6917(07)00208-5

Introduction

Khapalov, A. Y. (2012) · Advances in mathematical fluid mechanics · doi:10.1007/978-3-030-85285-6_1

Modeling Microtubule-Cytoplasm Interaction in Plant CellsPreprint

Murshed, M., Wei, D., Gu, Y., & Wang, J. (2022) · bioRxiv (Cold Spring Harbor Laboratory) · doi:10.1101/2022.09.29.510138

To Study the Effect of Confining Walls on Permeable, Flexible Planktonic Particle using Immersed Boundary Method

Panghal, R., Yadav, P., & Ghosh, S. (2024) · Current Materials Science · doi:10.2174/0126661454267045231226053357

Two dimensional simulations to study the relationship between settling velocity and flexibility of a particle

Panghal, R., Ghosh, S., & Sharma, A. K. (2024) · Physica Scripta · doi:10.1088/1402-4896/ad4d2b

Modeling straight and circle swimmers: from single swimmer to collective motion

Ventrella, F. M., Boffetta, G., Cencini, M., & Lillo, F. D. (2024) · The European Physical Journal E · doi:10.1140/epje/s10189-024-00458-z

Analysis of the Stability of an Immersed Elastic Surface Using the Method of Regularized StokesletsPreprint

Ferranti, D., & Olson, S. D. (2025) · SSRN Electronic Journal · doi:10.2139/ssrn.5363461

Invertebrate Locomotor Systems

Full, R. J. (1996) · Comprehensive physiology · doi:10.1002/j.2040-4603.1996.tb01737.x

Filiform microswimmers in tubular confinements

Morshed, A., Cortez, R., & Fauci, L. (2025) · Physical Review Fluids · doi:10.1103/7t6v-w8sv

Research on the capturing process of yarn-end using lattice Boltzmann method

Wang, X., Meng, Z., Liu, L., & Cai, G. (2025) · Physics of Fluids · doi:10.1063/5.0306273

Analysis of the stability of an immersed elastic surface using the method of regularized Stokeslets

Ferranti, D., & Olson, S. D. (2026) · Journal of Computational Physics · doi:10.1016/j.jcp.2025.114636

A computational model for three-phase fluid-structure interaction and its application to cellulose microfibril dynamics

Murshed, M., & Wang, J. (2026) · Computational and Mathematical Biophysics · doi:10.1515/cmb-2025-0033

Modèle de frontières immergées pour la simulation d'écoulements de fluide en interaction avec des structures poreuses

Pepona, M. (2016) · doi:10.70675/757c5efaz6dcez4ff5zac3dz700c52f21e18

Modeling and simulation of individual and collective swimming mechanisms in active suspensions

Delmotte, B. (2015) · doi:10.70675/1d16718czeeacz4505z8157z3cd50bb27732

Analyse et contrôle de modèles d'écoulements fluides

Savel, M. (2017) · doi:10.70675/57887678z2b6cz423cz9c76z49dc5a99e99e

Simulation numérique du ballottement d'ergol et modélisation de l'interaction fluides-membrane dans un réservoir de satellite

Dalmon, A. (2018) · doi:10.70675/8ca083bez70c0z48fbz88b5z1a427f457785

Développement de méthodes des frontières immergées pour l’étude de problèmes couplés fluide-structure

Ménez, L. (2024) · doi:10.70675/8c101e61z0031z409fz91bdzfb9c2348e6b4

Undulatory swimming in lyotropic liquid crystal polymers at finite Reynolds numbers

Quan, Y., Gao, T., Xia, Y., Yu, Z., Chen, S., & Lin, Z. (2026) · Journal of Fluid Mechanics · doi:10.1017/jfm.2026.12124

Near-wall locomotion of an elastic undulatory swimmer in finitely extensible nonlinear elastic-Peterlin fluids

Liang, J., Quan, Y., Fan, P., Xia, Y., Zhang, J., & Lin, Z. (2026) · Journal of Fluids and Structures · doi:10.1016/j.jfluidstructs.2026.104738

Reynolds number limits for jet propulsion: A numerical study of simplified jellyfish

Herschlag, G., & Miller, L. A. (2010) · arXiv · doi:10.48550/arxiv.1010.3357

Simulation of Propulsive Dynamics of an Organism in a Viscous Fluid Using an Immersed Boundary Finite Volume Method

Maniyeri, R. (2014) · Applied Mechanics and Materials · doi:10.4028/www.scientific.net/amm.592-594.1945 · Cited by 4

An efficient algorithm for simulation of forced deformable bodies interacting with incompressible flows; Application to fish swimming

Bontoux, P., Viazzo, S., Kai Schneider, B., & Ghaffari, S. A. (2014) · HAL · doi:10.13140/2.1.2976.1921

Modeling and simulation of fish-like swimming

Bergmann, M., & Iollo, A. (2010) · Journal of Computational Physics · doi:10.1016/j.jcp.2010.09.017 · Cited by 144

Numerical simulation of incompressible flows interacting with forced deformable bodies : Application to fish swimming

Dehkharghani, S. A. G. (2014) · doi:10.70675/aaa2a716z0d5az486cz9b6bz993d16a64746

Lagrangian Flow Skeletons Captured in the Wake of a Swimming Nematode C. elegans Using an Immersed Boundary Fluid-Structure Interaction Approach

Taheri, A. (2021) · Cited by 1