A Discontinuous Galerkin Discretization for the Intrinsic Beam Model

Abstract

With the Versatile Aeromechanic Simulation Tool (VAST), the German Aerospace Center (DLR) is developing a software framework for the simulation of rotary-wing aircraft. One challenge consists of simulating the dynamic behaviour of rotor blades. In general, rotor blades can be considered as flexible beams for which numerous models have been developed in the past. One of them is the geometrically exact intrinsic beam model derived by Hodges (AIAA J. 41(6):1131, 2003). It is represented by a time dependent hyperbolic system of partial differential equations (PDE) in one space dimension. In contrast to other well-known models like the EulerBernoulli model or the Timoschenko model, the governing equations of the intrinsic beam model contain non-linearities which makes it a geometrically exact model. This allows to model also beams undergoing large deflections making it well-suited for the simulation of rotor blades. We derive an energy stable discontinuous Galerkin (DG) approach for its discretization based on the approach in Kopriva and Gassner (SIAM J. Sci. Comput. 36(4):A2076, 2014).