Transfer of conservative discrete differential operators between staggered grids: construction and duality relations. (23rd June 2021)

• Record Type: Journal Article
• Authors: Goudon, Thierry; Krell, Stella; Llobell, Julie; Minjeaud, Sebastian
• Is Part Of: IMA journal of numerical analysis. Volume 42:Number 3(2022)
• Page Start: 2459
• Page End: 2504
• Publication Date: 2021-06-23
• Subjects: staggered grids -- finite volume method -- discrete duality finite volume -- divergence problem; Numerical analysis -- Periodicals; 519.405
• DOI: 10.1093/imanum/drab042
• Languages: English
• ISSNs: 0272-4979

Abstract

Abstract: This paper is concerned with the construction of a discrete conservative operator on a mesh, knowing a conservative operator on a different mesh. We analyse the possibility of defining such a transfer based on the preservation of conservation properties and provide practical procedures, which can be effectively implemented for schemes that work on staggered grids. We show that such a transfer can be applied to obtain a discrete balance equation on a mesh starting from a discrete balance equation on a different mesh, and to prove local discrete duality relations for standard discrete operators defined on staggered grids.