Premium
A block iterative finite element algorithm for numerical solution of the steady–state, compressible Navier–Stokes equations
Author(s) -
Cooke Charlie H.,
Blanchard Doris K.
Publication year - 1977
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/nme.1620111210
Subject(s) - finite element method , mathematics , mixed finite element method , extended finite element method , discontinuous galerkin method , iterative method , rate of convergence , pressure correction method , hp fem , mathematical analysis , compressibility , finite element limit analysis , mathematical optimization , computer science , physics , mechanics , computer network , channel (broadcasting) , thermodynamics
An iterative method for numerically solving the time independent Navier–Stokes equations for viscous compressible flows is presented. The method is based upon partial application of the Gauss–Seidel principle in block form to the systems of the non‐linear algebraic equations which arise in construction of finite element (Galerkin) models approximating solutions of fluid dynamic problems. The C 0 ‐cubic element on triangles is employed for function approximation. Computational results for a free shear flow at Re = 1000 indicate significant achievement of economy in iterative convergence rate over finite element and finite difference models which employ the customary time dependent equations and symptotic time marching procedure to steady solution. Numerical results are in excellent agreement with those obtained for the same test problem employing time marching finite element and finite difference solution techniques.