The extended finite element method for rigid particles in Stokes flow

By Gregory J. Wagner, Nicolas Moës, Wing Kam Liu, Ted Belytschko. 2001

153 citations recorded by the source corpus.

A new method for the simulation of particulate flows, based on the extended finite element method (X‐FEM), is described. In this method, the particle surfaces need not conform to the finite element boundaries, so that moving particles can be simulated without remeshing. The near field form of the fluid flow about each particle is built into the finite element basis using a partition of unity enrichment, allowing the simple enforcement of boundary conditions and improved accuracy over other methods on a coarse mesh. We present a weak form of the equations of motion useful for the simulation of freely moving particles, and solve example problems for particles with prescribed and unknown velocities. Copyright © 2001 John Wiley & Sons, Ltd.

Subfields: Computational Mechanics

View Paper: https://www.semanticscholar.org/paper/72d6835e3f9801eb981fa89c4b37c4ef3f3e7aa1

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In Computational Mechanics

Citations in the corpus

Rheology of red blood cell aggregation by computer simulation (2006, methodology): “[8,9] have modeled the shear flow with rigid particles with continuum enrichment methods.”
Modeling quasi-static crack growth with the extended finite element method Part I: Computer implementation (2003, unknown): “…is characterized by Dundurs parameters (Dundurs, 1969): a ¼ l 1 ðj 2 þ 1Þ À l 2 ðj 1 þ 1Þ l 1 ðj 2 þ 1Þ þ l 2 ðj 1 þ 1Þ ; b ¼ l 1 ðj 2 À 1Þ À l 2 ðj 1 À 1Þ l 1 ðj 2 þ 1Þ þ l 2 ðj 1 þ 1Þ ; ð3aÞ j i ¼ 3 À m i 1 þ m i ðplane stressÞ; 3 À 4m i ðplane strainÞ; 8 < : ð3bÞ where l i and m i are the…”
Enrichment of enhanced assumed strain approximations for representing strong discontinuities: addressing volumetric incompressibility and the discontinuous patch test (2004, methodology): “[11] adopted a similar approach by enriching a standard biquadratic-displacement bilinearpressure four node quadrilateral element.”
A multiscale projection method for the analysis of carbon nanotubes (2004, unknown): “[27] and has been successfully applied in multiple-scale problems involving strain localization [10], boundary layers [60] and coupling of finite elements with meshfree shape functions [59].”
A comparison of the extended finite element method with the immersed interface method for elliptic equations with discontinuous coefficients and singular sources (2006, methodology): “The X-FEM is a variation on the partition of unity method [10] and has been used for the solution of crack growth problems [11; 2; 17; 15], arbitrary fixed material interfaces and voids [16], solidification problems [5; 4], and modeling rigid particles in Stokes flow [18].”