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Isogeometric boundary integral analysis of drops and inextensible membranes in isoviscous flow. (English) Zbl 1390.76651

Summary: The boundary integral method (BIM) is applied to investigate the dynamics of a single drop and an inextensible membrane in isoviscous shear flow. The novelty of this work resides in the application of isogeometric analysis (IGA) to define the interface of the deformable objects. The employed B-spline basis functions facilitate the direct evaluation of surface normal vectors and curvatures, as required by the BIM. Collocation and \(L^2\)-projection methods are implemented to approximate the velocity of the B-spline control points. In particular, a comparison between these two methods for the case of the drop is reported and shows that the collocation method provides faster and more stable results. The collocation method is also applied for the determination of the surface tension in an inextensible membrane. A series of simulations is conducted to verify the isogeometric approach, and various computational aspects are studied.

MSC:

76M22 Spectral methods applied to problems in fluid mechanics
76D07 Stokes and related (Oseen, etc.) flows
65N35 Spectral, collocation and related methods for boundary value problems involving PDEs
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