Isogeometric boundary integral analysis of drops and inextensible membranes in isoviscous flow

• B-splines are used to evaluate surface gradients on deformable object interfaces.
• Two controlpoint-based geometry evolution strategies are proposed and examined.
• The collocation method yields stable results for the simulation of drop deformation.
• Isogeometric collocation is used to compute inextensible membrane surface tension.
• The stable inclination angle of inextensible membranes in shear flow is studied.

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 L2L2-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.