A finite volume method on NURBS geometries and its application in isogeometric fluid–structure interaction

A finite volume method for geometries parameterized by Non-Uniform Rational B-Splines (NURBS) is proposed. Since the computational grid is inherently defined by the knot vectors of the NURBS parameterization, the mesh generation step simplifies here greatly and furthermore curved boundaries are resolved exactly. Based on the incompressible Navier–Stokes equations, the main steps of the discretization are presented, with emphasis on the preservation of geometrical and physical properties. Moreover, the method is combined with a structural solver based on isogeometric finite elements in a partitioned fluid–structure interaction coupling algorithm that features a gap-free and non-overlapping interface even in the case of non-matching grids.