The Method of Regularized Stokeslets

By R. Cortez. SIAM Journal on Scientific Computing, 2001

489 citations recorded by the source corpus.

Subfields: Computational Mechanics, Mechanics of Materials, Ocean Engineering

View Paper: https://www.semanticscholar.org/paper/be74ba76fdfe4a37f960d9a2a0069a1560472f2c

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In Computational Mechanics

In Mechanics of Materials

In Ocean Engineering

Citations in the corpus

A boundary element regularized Stokeslet method applied to cilia- and flagella-driven flow (2009, methodology): “Cortez et al. (2005) showed that with the choice ψ (x−ξ) := 15 4/(8πμr7 ), the regularised Stokeslet velocity tensor is given by S ij(x, ξ) = δij(r 2 + 2 2) + rirj r3 .”
Human sperm accumulation near surfaces: a simulation study (2009, methodology): “…recent work has involved introducing a discrete viscoelastic structure to the two-dimensional domain (Dillon et al. 2007) and combining the immersed-boundary method with the regularized Stokeslet technique (Cortez 2001; Cortez, Fauci & Medovikov 2005) for the modelling of three-dimensional beating.”
On the order of accuracy of the immersed boundary method: Higher order convergence rates for sufficiently smooth problems (2005, methodology): “To our knowledge this is the first time that convergence rates in excess of first order have been documented using the immersed boundary method, although higher order convergence rates have been observed for related methods [10–13].”
Fluid dynamics of self-propelled microorganisms, from individuals to concentrated populations (2007, methodology): “…a force Fk/(x) centered at xk and using the regularizing function /ðxÞ ¼ 15e 4 8pðjxj2 þ e2Þ7=2 ; ð12Þ the resulting velocity is uðxÞ ¼ 1 8pl gk ðjx xkj2 þ e2Þ3=2 ; ð13Þ where gk ¼ ½jx xkj2 þ 2e2 Fk þ ½Fk ðx xkÞ ðx xkÞ: ð14Þ This is called a Regularized Stokeslet (Cortez 2001; Cortez et al. 2005).”
The hydrodynamics of swimming microorganisms (2008, methodology): “His modeling approach has been extended for filament motion near a solid boundary [117–120], and an alternative approach based on the method of regularized flow singularities [121] has also been devised [122].”
Dynamics of filaments and membranes in a viscous fluid (2009, background): “Representative examples include work by Shelley and Ueda (2000) and Cortez (2001).”
Hydrodynamic propulsion of human sperm (2009, methodology): “Sij (sn, s) is the regularized stokeslet of Cortez (2001), which removes the singularity of the stokeslet.”
An augmented approach for Stokes equations with a discontinuous viscosity and singular forces (2007, methodology): “We refer the readers to [4,5,9,18,26,37] for various methods and the references therein.”
Physics of rheologically enhanced propulsion: Different strokes in generalized Stokes (2013, methodology): “These results raise three interesting questions: (1) is the viscosity differential always negative, reducing instantaneous velocity, for three-sphere swimmers, (2) will the coefficient of proportionality between the instantaneous velocity and the viscosity differential always be greater during the r”
ON THE ACCURACY OF FINITE DIFFERENCE METHODS FOR ELLIPTIC PROBLEMS WITH INTERFACES (2006, methodology): “In [13], Cortez derived analytic solutions for the one-fluid case where the enclosed boundary is a unit circle; see examples 4a and 4b in [13].”
Mammalian Sperm Motility: Observation and Theory (2011, methodology): “This early work has since motivated the development of slenderbody theory for Stokes flow (Lighthill 1976, Johnson 1980) and has influenced later advances such as the boundary integral method (Youngren & Acrivos 1975) and regularized stokeslets (Cortez 2001).”
Dynamics of Flexible Fibers in Viscous Flows and Fluids (2019, methodology): “A popular method for solving the Stokes equations is the method of regularized Stokeslets of [20] which uses superpositions of regularized fundamental solutions.”
Hydrodynamics of self-propulsion near a boundary: predictions and accuracy of far-field approximations (2012, methodology): “e in order to accommodate the slip velocity u s. We brie y recount the method of images with regularized Stokeslets as presented by Ainley et al. (2008) (itself a modication to the method derived by Cortez 2002). The surface is discretized by Mpoints, located at xk;0 for k= 1;2;:::;M. For a given po”