Galerkin boundary integral formulation for axisymmetric stokes flow. (November 2017)

• Record Type: Journal Article
• Authors: Xue, A.; Graciani, E.; Gray, L.J.; Mantič, V.; Garzon, Maria
• Is Part Of: Engineering analysis with boundary elements. Volume 84(2017)
• Page Start: 178
• Page End: 185
• Publication Date: 2017-11
• Subjects: Stokes flow -- Axisymmetry -- Galerkin approximation -- Singular integration; Boundary element methods -- Periodicals; Engineering mathematics -- Periodicals; Équations intégrales de frontière, Méthodes des -- Périodiques; Mathématiques de l'ingénieur -- Périodiques; Boundary element methods; Engineering mathematics; Periodicals; 620.00151
• DOI: 10.1016/j.enganabound.2017.08.009
• Languages: English
• ISSNs: 0955-7997

Abstract

Abstract: A Galerkin boundary integral formulation for 3D axisymmetric Stokes flow is presented. The singular integrals are evaluated by splitting the complicated Green's function kernels into a singular term that can be integrated analytically, plus a term for which Gauss quadrature provides sufficient accuracy. As in a previous axisymmetric Laplace implementation, the treatment of the additional on-axis singularity is aided by employing a modified Galerkin weight function, and a similar splitting method is then employed to handle this singularity. The target application of the Stokes algorithm is to model the breakup of one viscous fluid enclosed inside a second, and this two fluid problem can be formulated in terms of a single boundary integral equation along the interface. The Galerkin form for this equation is derived herein.