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A non-linearly stable implicit finite element algorithm for hypersonic aerodynamics

Authors :
Iannelli, G. S
Baker, A. J
Source :
International Journal for Numerical Methods in Engineering. 34
Publication Year :
1992
Publisher :
United States: NASA Center for Aerospace Information (CASI), 1992.

Abstract

A generalized curvilinear coordinate Taylor weak statement implicit finite element algorithm is developed for the two-dimensional and axisymmetric compressible Navier-Stokes equations for ideal and reacting gases. For accurate hypersonic simulation, air is modeled as a mixture of five perfect gases, i.e., molecular and atomic oxygen and nitrogen as well as nitric oxide. The associated pressure is then determined via Newton solution of the classical chemical equilibrium equation system. The directional semidiscretization is achieved using an optimal metric data Galerkin finite element weak statement, on a developed 'companion conservation law system', permitting classical test and trial space definitions. Utilizing an implicit Runge-Kutta scheme, the terminal algorithm is then nonlinearly stable, and second-order accurate in space and time on arbitrary curvilinear coordinates. Subsequently, a matrix tensor product factorization procedure permits an efficient numerical linear algebra handling for large Courant numbers. For ideal- and real-gas hypersonic flows, the algorithm generates essentially nonoscillatory numerical solutions in the presence of strong detached shocks and boundary layer-inviscid flow interactions.

Subjects

Subjects :
Aerodynamics

Details

Language :
English
ISSN :
00295981
Volume :
34
Database :
NASA Technical Reports
Journal :
International Journal for Numerical Methods in Engineering
Notes :
NAS2-12568
Publication Type :
Report
Accession number :
edsnas.19920048863
Document Type :
Report