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Finite element method in the solution of the Euler and Navier‐Stokes equations for internal flow
Author(s) -
Habashi W. G.,
Baruzzi G.,
Peeters M. F.,
Hafez M. M.
Publication year - 1991
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.1690070207
Subject(s) - inviscid flow , mathematics , backward euler method , euler equations , finite element method , discretization , semi implicit euler method , transonic , mathematical analysis , generalized minimal residual method , euler's formula , euler method , discontinuous galerkin method , linear system , aerodynamics , classical mechanics , mechanics , physics , thermodynamics
Finite element solutions of the Euler and Navier‐Stokes equations are presented, using a simple dissipation model. The discretization is based on the weak‐Galerkin weighted residual method and equal interpolation functions for all the unknowns are permitted. The nonlinearity is iterated upon using a Newton method and at each iteration the linear algebraic system is solved by a direct solver with all unknowns fully coupled. Results are presented for two‐dimensional transonic inviscid flows and two‐ and three‐dimensional incompressible viscous flows. Convergence of the algorithm is shown to be quadratic, reaching machine accuracy in very few iterations. The inviscid results demonstrate the existence of nonunique numerical solutions to the steady Euler equations.