Convergence to steady-state solutions for stabilized finite element simulations of compressible flows

Computers and Mathematics with Applications

Volumn 40, Issue 4, 2000, Pages 625-643

  Banas K ^a  

^a CRACOW UNIVERSITY OF TECHNOLOGY   (Poland)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; COMPRESSIBLE FLOW; COMPUTER SIMULATION; FINITE ELEMENT METHOD; INTEGRATION; ITERATIVE METHODS; LINEAR EQUATIONS; PROBLEM SOLVING;

EULER EQUATIONS; PSEUDOTIME INTEGRATION; STEADY STATE SOLUTIONS;

CONVERGENCE OF NUMERICAL METHODS;

EID: 0034249249     PISSN: 08981221     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0898-1221(00)00184-X     Document Type: Article

References (22)

1. A.N. Brooks and T.J.R. Hughes, Streamline upwind/Petrov-Galerkin formulations for convection dominated flows wuth the particular emphasis on the incompressible Navier-Stokes equations, Computer Methods in Applied Mechanics and Engineering 32, 199-259, (1982).
2. T.J.R. Hughes, L.P. Franca and M. Mallet, A new finite element formulation for computational fluid dynamics: I. Symmetric forms of the compressible Euler and Navier-Stokes equations and the second law of thermodynamics, Computer Methods in Applied Mechanics and Engineering 54, 223-234, (1986).
3. T.J.R. Hughes and M. Mallet, A new finite element formulation for computational fluid dynamics: III. The generalized streamline operator for multidimensional advective-diffusive systems, Computer Methods in Applied Mechanics and Engineering 58, 305-328, (1986).
4. T.J.R. Hughes and M. Mallet, A new finite element formulation for computational fluid dynamics: IV. A discontinuity-capturing operator for multidimensional advective-diffusive systems, Computer Methods in Applied Mechanics and Engineering 58, 329-336, (1986).
5. F. Shakib, T.J.R. Hughes and Z. Johan, A new finite element formulation for computational fluid dynamics: X. The compressible Euler and Navier-Stokes equations, Computer Methods in Applied Mechanics and Engineering 89, 141-219, (1991).
6. P. Hansbo and C. Johnson, Adaptive streamline diffusion method for compressible flow using conservation variables, Computer Methods in Applied Mechanics and Engineering 87, 267-280, (1991).
7. S.K. Aliabadi, S.E. Ray and T.E. Tezduyar, SUPG finite element computation of viscous compressible flows based on the conservation and entropy variables formulations, Computational Mechanics 11, 300-312, (1993).
8. C. Johnson, A. Szepessy and P. Hansbo, On the convergence of shock-capturing streamline diffusion finite element methods for hyperbolic conservation laws, Mathematics of Computation 54, 107-129, (1990).
9. K. Eriksson and C. Johnson, Adaptive streamline diffusion finite element methods for stationary convection diffusion problems, Mathematics of Computation 60, 167-188, (1993).
10. P. Hansbo, Explicit streamline diffusion finite element methods for the compressible euler equations in conservation variables, Journal of Computational Physics 109, 274-288, (1993).
11. J.-C. Carette, H. Deconinck, H. Paillere and P.L. Roe, Multidimensional upwinding: Its relation to finite elements, International Journal for Numerical Methods in Engineering 20, 935-955, (1995).
12. K. Banaś and L. Demkowicz, Entropy controlled adaptive finite element simulations for compressible gas flow, Journal of Computational Physics 126, 181-201, (1996).
13. C. Hirsch, Numerical Computation of Internal and External Flows, Wiley, Chichester, (1988).
14. L. Demkowicz, J.T. Oden, W. Rachowicz and O. Hardy, An h-p Taylor-Galerkin finite element method for compressible Euler equations, Computer Methods in Applied Mechanics and Engineering 88, 363-396, (1991).
15. W. Rachowicz, An h-Adaptive Finite Element Method for Solving Compressible Navier-stokes Equations, (In Polish), Insitute of Fundamental Technological Research Press, Warszawa, (1997).
16. A. Safjan and J.T. Oden, High-order Taylor-Galerkin methods for linear hyperbolic systems, Journal of Computational Physics 120, 206-230, (1995).
17. L. Demkowicz, J.T. Oden, W. Rachowicz and O. Hardy, Towards a universal h-p adaptive finite element strategy, Part 1. Constrained approximation and data structure, Computer Methods in Applied Mechanics and Engineering 77, 79-112, (1989).
18. L. Demkowicz, J.T. Oden and W. Rachowicz, A new finite element method for solving compressible Navier- stokes equations based on an operator splitting method and h-p adaptivity, Computer Methods in Applied Mechanics and Engineering 84, 275-326, (1990).
19. Y. Saad and M. Schultz, GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems, SIAM Journal of Scientific and Statistical Computing 7, 856-869, (1986).
20. W. Rachowicz, An anisotropic h-adaptive finite element method for compressible Navier-Stokes equations, Computer Methods in Applied Mechanics and Engineering 146, 231-252, (1997).
21. Z. Johan and T.J.R. Hughes, A globally convergent matrix-free algorithm for implicit time-marching schemes arising in finite element analysis in fluids, Computer Methods in Applied Mechanics and Engineering 87, 281-304, (1991).
22. A. Dervieux, B.V. Leer, J. Periaux and A. Rizzi, Editors, Numerical Simulation of Compressible Euler Flows, Vieweg, Braunschweig, (1989).