Equivalence conditions for the finite volume and finite element methods in spherical coordinates

D. De Santis, G. Geraci and A. Guardone

Mathematics and Computers in Simulation (MATCOM), 2014, vol. 106, issue C, 60-75

Abstract: A numerical technique for the solution of the compressible flow equations over unstructured grids in a spherical reference is presented. The proposed approach is based on a mixed finite volume/finite element discretization in space. Equivalence conditions relating the finite volume and the finite element metrics in spherical coordinates are derived. Numerical simulations of the explosion and implosion problems for inviscid compressible flows are carried out to evaluate the correctness of the numerical scheme and compare fairly well to one-dimensional simulations over very fine grids.

Keywords: Compressible flows; Shock waves; Explosion/implosion problem; Spherical coordinates; Finite element/volume methods (search for similar items in EconPapers)
Date: 2014
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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:106:y:2014:i:c:p:60-75

DOI: 10.1016/j.matcom.2012.04.010

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