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Numerical solution of the Navier‐Stokes equations using a finite element method
Author(s) -
Mehta R. C.,
Jayachandran T.,
Sastri V. M. K.
Publication year - 1991
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.1650130406
Subject(s) - finite element method , mathematics , shock (circulatory) , navier–stokes equations , smoothing , boundary value problem , boundary layer , numerical analysis , computation , mathematical analysis , mechanics , algorithm , physics , medicine , statistics , compressibility , thermodynamics
A finite element algorithm for solving the Navier‐Stokes equations is presented for the analysis of high‐speed viscous flows. The algorithm uses triangular elements. The unsteady equations are integrated to steady state with a Runge‐Kutta time‐marching scheme. A postprocessing artificial dissipation term is introduced to stabilize the computations and to dampen dissipation errors. Numerical results are compared with the calculation of uniform flow on a rectangular region which encounters an embedded oblique shock. A shock/turbulent boundary layer problem is also solved and results are compared with experimental data. It is shown that the postprocessing smoothing term and boundary conditions similar to the finite difference method work well in the present numerical studies.