Locally conservative projection methods: benchmarking and practical implementation

Abstract

Purpose – This article presents a locally conservative projection method which aims to preserve the integral of a function and one operator among grad, div, or curl. Design/methodology/approach – After a theoretical description of the projection methods, the locally conservative projection is analytically tested and compared with the orthogonal method. In the second part, the implementation of the methods is described, and improvements are proposed. An industrial application of the present work, consisting in a magneto-thermal coupled problem, is then presented. Findings – The implementation of the conservative method is simpler than the implementation of the orthogonal method while presenting similar behaviour in terms of accuracy and conservation. Originality/value – The locally conservative method is extended to curl-conform and div-conform elements. Furthermore, three-dimensional studies are proposed.