Numerical Integration of Fluid Power Circuit Models Using Two-Stage Semi-Implicit Runge-Kutta Methods

Fluid power circuits that contain fluid volumes of different orders of magnitude are difficult to simulate because the system of ordinary differential equations is numerically stiff. Even algorithms specially designed for stiff systems require excessively small time steps to avoid numerical oscillation in simulations of some circuits. In this paper the accuracy and numerical stability of several two-stage semi-implicit Runge-Kutta methods that have been proposed in circuit simulation literature are analysed and compared. It is shown that, for integration of very stiff circuits, the best method in this class is an L-stable method. A simple numerical example is used to verify the theoretical results. The example includes a novel way of modelling orifice flow that is especially suitable for numerical simulations.