Energy-based numerical prediction of electrohydraulic shock wave via a two-stage algorithm

Abstract

Electrohydraulic shock waves (EHSWs) from pulsed discharges in liquids are used in diverse applications, where the peak pressure is particularly critical for inducing mechanical impacts. However, accurate numerical prediction of shock wave profiles typically requires high-performance computing, which limits routine use for end users. This paper presents a two-stage algorithm for the prediction of EHSWs generated by high-current pulsed discharges in weakly compressible liquids. Stage 1 computes the temporal evolution of the discharge channel and the pressure using energy-based equations with a coarse time step. Stage 2 reconstructs the spatial pressure distribution under an acoustic approximation and a cylindrical piston representation, enabling rapid evaluation with minimal computational cost within the intended operating regime. The approach is validated against two experiments: a high-current pulsed discharge and a current-interception configuration, while maintaining <2.5 % error in peak pressure across parameter sets. Parametric analysis further highlights that effective energy unifies the scaling of peak pressure across circuits, providing actionable guidance for circuit design under typical high-current discharge conditions.