Validation of a 2D cell-centered Finite Volume method for elliptic equations

Gung-Min Gie, Chang-Yeol Jung and Thien Binh Nguyen

Mathematics and Computers in Simulation (MATCOM), 2019, vol. 165, issue C, 119-138

Abstract: Following the approach in Gie and Temam(2010) and Gie and Temam(2015), we construct the Finite Volume (FV) approximations of a class of elliptic equations and perform numerical computations where a 2D domain is discretized by convex quadrilateral meshes. The FV method with Taylor Series Expansion Scheme (TSES), which is properly adjusted from a version widely used in engineering, is tested in a box, annulus, and in a domain which includes a topography at the bottom boundary. By comparing with other related convergent FV schemes in Sheng and Yuan(2008), Aavatsmark(2002), Hermeline(2000) and Faureet al. (2016), we numerically verify that our FV method is a convergent 2nd order scheme that manages well the complex geometry. The advantage of our scheme is on its simple structure which do not require any special reconstruction of dual type mesh for computing the nodal approximations or discrete gradients.

Keywords: Finite Volume method; Taylor series expansion scheme (TSES); Convergence and stability; Convex quadrilateral meshes (search for similar items in EconPapers)
Date: 2019
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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:165:y:2019:i:c:p:119-138

DOI: 10.1016/j.matcom.2019.03.008

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