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UNIFIED CONSTRUCTION OF FINITE ELEMENT AND FINITE VOLUME DISCRETIZATIONS FOR COMPRESSIBLE FLOWS
Author(s) -
SELMIN V.,
FORMAGGIA L.
Publication year - 1996
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/(sici)1097-0207(19960115)39:1<1::aid-nme837>3.0.co;2-g
Subject(s) - finite element method , finite volume method , compressibility , euler equations , grid , mathematics , computer science , metric (unit) , euler's formula , mathematical optimization , equivalence (formal languages) , mixed finite element method , compressible flow , topology (electrical circuits) , geometry , mathematical analysis , engineering , structural engineering , discrete mathematics , mechanics , physics , operations management , combinatorics , aerospace engineering
A framework for the construction of node‐centred schemes to solve the compressible Euler and Navier–Stokes equations is presented. The metric quantities are derived by exploiting some properties of C 0 finite element shape functions. The resulting algorithm allows to implement both artificial diffusion and one‐dimensional upwind‐type discretizations. The proposed methodology adopts a uniform data structure for diverse grid topologies (structured, unstructured and hybrid) and different element shapes, thus easing code development and maintenance. The final schemes are well suited to run on vector/parallel computer architectures. In the case of linear elements, the equivalence of the proposed method with a particular finite volume formulation is demonstrated.