Mixed time–frequency domain simulation of a hydraulic inductance pipe with a check valve

This paper deals with the efficient computation of hydraulic switching systems with a check valve by a mixed time–frequency domain method; frequency-domain modelling is performed on the wave propagation in a pipe and time-domain modelling is applied to the switching valve and the check valve. The dual property of the check valve makes the complete problem have variational inequality properties. A solution method is presented which replaces the pressure and the flowrate of the check valve as a function of one new variable. The resulting system of non-linear algebraic equations is solved using a Newton–Raphson method in combination with a smoothing of the non-smooth properties of the check valve. The method is applied to a parameter study of a hydraulic buck converter.