Augmenting numerical stability of the Galerkin finite element formulation for electromagnetic flowmeter analysis

Abstract

Due to the complexities in handling liquid metals, theoretical evaluation of the sensitivity of magnetic flowmeters forms an attractive and preferred choice. The classical Galerkin finite element formulation is generally opted for the required evaluation. However, it is known to lead to numerical oscillations at higher flow rates. To overcome this, modified methods like upwind/Petrov–Galerkin schemes are generally suggested in allied areas like fluid dynamics. However, it requires the evaluation of stabilisation parameter and this parameter is not readily available for elements of order beyond quadratic. After a careful analysis of the numerical instability through a reduced one-dimensional problem, an elegant and stable approach is devised. In this scheme, the input magnetic field is restated in terms of the associated vector potential and the classical Galerkin finite element method is employed without any modification. The analytical solution of the associated difference equation is employed to show: (i) the stability of the proposed approach at higher flow rates and (ii) quantification of the small oscillations remnant at intermediate flow rates. It is then applied to the original flowmeter problem and the stability of the numerical solution is clearly demonstrated.