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Finite element/finite volume solutions of full potential, Euler and Navier‐Stokes equations for compressible and incompressible flows
Author(s) -
Hafez M.
Publication year - 1995
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/fld.1650200804
Subject(s) - euler equations , inviscid flow , finite volume method , compressible flow , finite element method , compressibility , mathematics , pressure correction method , incompressible flow , mathematical analysis , physics , mechanics , thermodynamics
A cell‐vertex finite volume formulation, using local finite element approximations to calculate fluxes through an auxiliary mesh (control volumes) is used to solve inviscid and viscous compressible flow equations on unstructured grids. Non‐linear artificial viscosity methods are adopted to avoid decoupling and capture shock waves. Artificial time‐dependent terms are augmented if needed, to guarantee convergence of common iterative procedures to a steady‐state solution. The incompressible limit of compressible flow equations is studied. A unified approach for solving both compressible and incompressible flow problems is proposed. Also some results of a zonal formulation with different governing equations in different regions are presented. Applications to the solution of Maxwell's equations for wave propagation and scattering are discussed in an appendix.