Half-Explicit Exponential Runge–Kutta Methods for Index-1 DAEs in Helicopter Simulation

In this paper we suggest a combination of exponential integrators and half-explicit Runge–Kutta methods for solving index-1 DAE systems with a stiff linear part in their differential equations. We discuss the behavior of the resulting half-explicit exponential Runge–Kutta (HEERK) methods for a simple numerical example and for a coupled rotor simulation. The coupled rotor simulation is based on a modular software design where all subsystems are modeled by ODEs in state-space form. By connecting the subsystems’ inputs and outputs we obtain an index-1 DAE system. Large terms in the system can be expressed as a stiff linear part which includes strong damping or oscillation terms as well as coefficients for the discretization of the rotor blades (3d beam equations). We show that the proposed HEERK methods can solve the resulting system efficiently with a reasonable timestep size.