Comments on 'Adiabatic shock capturing in perfect gas hypersonic flows'

International Journal for Numerical Methods in Fluids

Volumn 66, Issue 7, 2011, Pages 935-938

  Tezduyar, Tayfun E ^a  

^a Rice University   (United States)

Author keywords

Compressible flows; Shock capturing; Shock capturing parameter; Stabilization parameters; SUPG formulation

Indexed keywords

PERFECT GAS; SHOCK CAPTURING; STABILIZATION PARAMETERS; SUPG FORMULATION;

HYPERSONIC FLOW; STABILIZATION;

COMPRESSIBLE FLOW;

EID: 79957899520     PISSN: 02712091     EISSN: 10970363     Source Type: Journal    
DOI: 10.1002/fld.2293     Document Type: Article

References (27)

1. Tezduyar TE, Hughes TJR. Development of time-accurate finite element techniques for first-order hyperbolic systems with particular emphasis on the compressible Euler equations. NASA Technical Report NASA-CR-204772, NASA, 1982. Available from:
2. Tezduyar TE, Hughes TJR. Finite element formulations for convection dominated flows with particular emphasis on the compressible Euler equations. Proceedings of AIAA 21st Aerospace Sciences Meeting, AIAA Paper 83-0125, Reno, Nevada, 1983.
3. Hughes TJR, Tezduyar TE. Finite element methods for first-order hyperbolic systems with particular emphasis on the compressible Euler equations. Computer Methods in Applied Mechanics and Engineering 1984; 45:217-284.
4. Hughes TJR, Mallet M. 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 1986; 58:329-339.
5. Hughes TJR, Franca LP, Mallet M. A new finite element formulation for computational fluid dynamics: VI. Convergence analysis of the generalized SUPG formulation for linear time-dependent multi-dimensional advective-diffusive systems. Computer Methods in Applied Mechanics and Engineering 1987; 63:97-112.
6. Le Beau GJ, Tezduyar TE. Finite element computation of compressible flows with the SUPG formulation. Advances in Finite Element Analysis in Fluid Dynamics, vol. FED-123. ASME: New York, 1991; 21-27.
7. Le Beau GJ, Ray SE, Aliabadi SK, Tezduyar TE. SUPG finite element computation of compressible flows with the entropy and conservation variables formulations. Computer Methods in Applied Mechanics and Engineering 1993; 104:397-422.
8. Tezduyar TE, Park YJ. Discontinuity capturing finite element formulations for nonlinear convection-diffusion-reaction equations. Computer Methods in Applied Mechanics and Engineering 1986; 59:307-325.
9. Hughes TJR, Brooks AN. A multi-dimensional upwind scheme with no crosswind diffusion. In Finite Element Methods for Convection Dominated Flows, Hughes TJR (ed.), AMD-Vol.34. ASME: New York, 1979; 19-35.
10. Brooks AN, Hughes TJR. Streamline upwind/Petrov-Galerkin formulations for convection dominated flows with particular emphasis on the incompressible Navier-Stokes equations. Computer Methods in Applied Mechanics and Engineering 1982; 32:199-259.
11. Tezduyar TE, Osawa Y. Finite element stabilization parameters computed from element matrices and vectors. Computer Methods in Applied Mechanics and Engineering 2000; 190:411-430.
12. Catabriga L, Coutinho ALGA, Tezduyar TE. Compressible flow SUPG stabilization parameters computed from element-edge matrices. Computational Fluid Dynamics Journal 2004; 13:450-459.
13. Catabriga L, Coutinho ALGA, Tezduyar TE. Compressible flow SUPG parameters computed from element matrices. Communications in Numerical Methods in Engineering 2005; 21:465-476.
14. Catabriga L, Coutinho ALGA, Tezduyar TE. Compressible flow SUPG parameters computed from degree-of-freedom submatrices. Computational Mechanics 2006; 38:334-343.
15. Tezduyar TE. Finite element methods for fluid dynamics with moving boundaries and interfaces. In Encyclopedia of Computational Mechanics, Chapter 17, Stein E, Borst RD, Hughes TJR (eds), Fluids, vol. 3. Wiley: New York, 2004.
16. Tezduyar TE. Determination of the stabilization and shock-capturing parameters in SUPG formulation of compressible flows. Proceedings of the European Congress on Computational Methods in Applied Sciences and Engineering, ECCOMAS 2004 (CD-ROM), Jyvaskyla, Finland, 2004.
17. Tezduyar TE, Senga M. Determination of the shock-capturing parameters in SUPG formulation of compressible flows. Proceedings of the 6th World Congress on Computational Mechanics (CD-ROM), Beijing, China, 2004.
18. Tezduyar TE, Senga M. Stabilization and shock-capturing parameters in SUPG formulation of compressible flows. Computer Methods in Applied Mechanics and Engineering 2006; 195:1621-1632.
19. Tezduyar TE, Senga M. SUPG finite element computation of inviscid supersonic flows with YZβ shock-capturing. Computers and Fluids 2007; 36:147-159.
20. Tezduyar TE, Senga M, Vicker D. Computation of inviscid supersonic flows around cylinders and spheres with the supg formulation and YZβ shock-capturing. Computational Mechanics 2006; 38:469-481.
21. Rispoli F, Saavedra R, Corsini A, Tezduyar TE. Computation of inviscid compressible flows with the V-SGS stabilization and YZβ shock-capturing. International Journal for Numerical Methods in Fluids 2007; 54:695-706.
22. Corsini A, Rispoli F, Santoriello A. A variational multiscale high-order finite element formulation for turbomachinery flow computations. Computer Methods in Applied Mechanics and Engineering 2005; 194:4797-4823.
23. Rispoli F, Saavedra R. A stabilized finite element method based on SGS models for compressible flows. Computer Methods in Applied Mechanics and Engineering 2006; 196:652-664.
24. Rispoli F, Saavedra R, Menichini F, Tezduyar TE. Computation of inviscid supersonic flows around cylinders and spheres with the V-SGS stabilization and YZβ shock-capturing. Journal of Applied Mechanics 2009; 76:021209.
25. Catabriga L, de Souza DAF, Coutinho ALGA, Tezduyar TE. 3D Edge-based SUPG computation of inviscid compressible flows with YZβ shock-capturing. Journal of Applied Mechanics 2009; 76:021208.
26. Bazilevs Y, Calo VM, Tezduyar TE, Hughes TJR. YZβ discontinuity-capturing for advection-dominated processes with application to arterial drug delivery. International Journal for Numerical Methods in Fluids 2007; 54:593-608.
27. Tezduyar TE. Computation of moving boundaries and interfaces and stabilization parameters. International Journal for Numerical Methods in Fluids 2003; 43:555-575.