Fast Calculation of Stiff Hydraulic Models Using the Modified Pseudo-Dynamic Solver

Abstract

The work addresses the problem of the fast and accurate calculation of the mathematically stiff hydraulic models using the modified pseudo-dynamic solver (PDS). In particular, it studies which of the numerical integration methods inside the modified PDS ensure efficient calculation of the stiff hydraulic model. In the work, the operating principle of the modified PDS is described. The effect of the three different fixed-step integration methods (Euler, Runge-Kutta of fourth order, and modified Heun’s method) are considered. The numerical stability of the modified Heun’s method is improved by substituting the purely turbulent orifice model with the two-regime orifice model. The two-regime orifice accounts for both the turbulent and laminar flows and thus allows to avoid the numerical problems related to the small pressure drops. As a numerical example of the mathematically stiff hydraulic model a hydraulic circuit with the two-way flow control valve which contains small volume is employed. As the implementation environment for the developed simulation models the compiled C language that supports the real-time simulation is chosen. The solutions obtained for the numerical example using the modified PDS based on the three integration methods, their accuracies and calculation speeds are presented in comparison with the solution obtained using conventional integration procedure. The obtained results show that, in general, the modified PDS allows to solve numerically stiff hydraulic models in a very efficient way ensuring accelerated simulation with the high solution accuracy. It is also shown that the simulation speed-up can be obtained not only by the complexity reduction of the numerical integration method employed inside the modified PDS but also by increasing its numerical stability.