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This article presents two mathematical methods of derivation of the Laplace operator in a given curvilinear co-ordinate system. This co-ordinate system is defined in the area between the armature and the yoke of a high-speed solenoid valve (HSV). The Laplace operator can further be used for the numerical solving of the Laplace’s equation in order to determine the electromagnetic force acting on the armature of the HSV. In further steps the author derived an expression for the gradient and the vector surface element of the armature side surface in this co-ordinate system. The solution of the derivation was compared with one other solution derived in the past for the computational investigations on HSVs.

Re-derivation of Laplace operator on curvilinear coordinates used for the computation of force acting in solenoid valves