A generalized view on Galilean invariance in stabilized compressible flow computations

International Journal for Numerical Methods in Fluids

Volumn 64, Issue 10-12, 2010, Pages 1065-1083

  Scovazzi, G ^a   Love, E ^a  

^a SANDIA NATIONAL LABORATORIES   (United States)

Author keywords

Galilean transformations; Invariance; Stabilized methods; SUPG methods; Variational multi scale methods

Indexed keywords

DISCONTINUITY CAPTURING; GALILEAN INVARIANCE; GALILEAN TRANSFORMATION; GENERAL APPROACH; KEY ISSUES; MATRIX; MULTISCALE METHOD; OPERATOR DESCRIPTION; PUBLIC DOMAINS; STABILIZED METHOD; SUPG METHODS;

LINEAR TRANSFORMATIONS;

COMPRESSIBLE FLOW;

EID: 78649665578     PISSN: 02712091     EISSN: 10970363     Source Type: Journal    
DOI: 10.1002/fld.2417     Document Type: Article

References (35)

1. Scovazzi G. A discourse on Galilean invariance and SUPG-type stabilization. Computer Methods in Applied Mechanics and Engineering 2007; 196(4-6):1108-1132.
2. Scovazzi G. Galilean invariance and stabilized methods for compressible flows. International Journal for Numerical Methods in Fluids 2007; 54(6-8):757-778.
3. Scovazzi G. Stabilized shock hydrodynamics: II. Design and physical interpretation of the SUPG operator for Lagrangian computations. Computer Methods in Applied Mechanics and Engineering 2007; 196(4-6):966-978.
4. Scovazzi G, Christon MA, Hughes TJR, Shadid JN. Stabilized shock hydrodynamics: I. A Lagrangian method. Computer Methods in Applied Mechanics and Engineering 2007; 196(4-6):923-966.
5. Storti MA, Nigro NN, Paz RR, Dalcin LD, Rios Rodriguez GA, Lopez E. Fluid-structure interaction with a staged algorithm. Mecánica Computacional, volume XXV, Cardona A, Nigro N, Sonzogni V, Storti MA (eds). Asociatión Argentina de Mecánica Computacional: Santa Fe, 2006; 887-905. Available from.
6. 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.
7. Hughes TJR. Multiscale phenomena: Green's functions, the Dirichlet-to-Neumann formulation, subgrid-scale models, bubbles and the origin of stabilized methods. Computer Methods in Applied Mechanics and Engineering 1995; 127:387-401.
8. Hughes TJR, Feijóo GR, Mazzei L, Quincy J-B. The variational multiscale method-a paradigm for computational mechanics. Computer Methods in Applied Mechanics and Engineering 1998; 166:3-24.
9. Hughes TJR, Mazzei L, Jansen KE. Large eddy simulation and the variational multiscale method. Computing and Visualization in Science 2000; 3(47):147-162.
10. Hughes TJR, Mazzei L, Oberai AA, Wray AA. The multiscale formulation of large eddy simulation: decay of homogenous isotropic turbulence. Physics of Fluids 2001; 13:505-512.
11. Hughes TJR, Oberai AA, Mazzei L. Large eddy simulation of turbulent channel flows by the variational multiscale method. Physics of Fluids 2001; 13(6):1784-1799.
12. Hughes TJR, Scovazzi G, Franca LP. Multiscale and stabilized methods. In Encyclopedia of Computational Mechanics, Stein E, de Borst R, Hughes TJR (eds). Wiley: New York, 2004.
13. 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.
14. Hughes TJR, Franca LP, Mallet M. 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 1986; 54:223-234.
15. 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 2006; 195:1621-1632.
16. Shakib F, Hughes TJR, Johan Z. A new finite element formulation for computational fluid dynamics: X. The compressible Euler and Navier-Stokes equations. Computer Methods in Applied Mechanics and Engineering 1991; 89:141-219.
17. Hauke G. Simple stabilizing matrices for the computation of compressible flows in primitive variables. Computer Methods in Applied Mechanics and Engineering 2001; 190:6881-6893.
18. Hauke G, Hughes TJR. A unified approach to compressible and incompressible flows. Computer Methods in Applied Mechanics and Engineering 1994; 113:389-396.
19. Hauke G, Hughes TJR. A comparative study of different sets of variables for solving compressible and incompressible flows. Computer Methods in Applied Mechanics and Engineering 1998; 153:1-44.
20. Tezduyar TE, Aliabadi SK, Behr M, Mittal S. Massively parallel finite element simulation of compressible and incompressible flows. Computer Methods in Applied Mechanics and Engineering 1994; 119:157-177.
21. Tezduyar T, Aliabadi S, Behr M, Johnson A, Kalro V, Litke M. Flow simulation and high performance computing. Computational Mechanics 1996; 18:397-412.
22. Mittal S, Tezduyar TE. A unified finite element formulation for compressible and incompressible flows using augmented conservation variables. Computer Methods in Applied Mechanics and Engineering 1998; 161:229-243.
23. Tezduyar TE, Senga M. Stabilization and shock-capturing parameters in SUPG formulation of compressible flows. Computer Methods in Applied Mechanics and Engineering 1993; 104:397-422.
24. Cattabriga L, Coutinho ALGA, Tezduyar TE. Compressible flow SUPG stabilization parameters computed from degree-of-freedom submatrices. Computational Mechanics 2006; 38:334-343.
25. Tezduyar TE, Senga M, Vicker D. Computation of inviscid supersonic flows around cylinders and spheres with the SUPG formulation and YZ β shock-capturing. Computational Mechanics 2006; 38:469-481.
26. Masud A, Hughes TJR. A space-time Galerkin/least-squares finite element formulation of the Navier-Stokes equations for moving domain problems. Computer Methods in Applied Mechanics and Engineering 1997; 146:91-126.
27. Masud A. Effects of mesh motion on the stability and convergence of ALE based formulations for moving boundary flows. Computational Mechanics 2006; 38(4-5):430-439.
28. Lesoinne M, Farhat C. Geometric conservation laws for flow problems with moving boundaries and deformable meshes, and their impact on aeroelastic computations. Computer Methods in Applied Mechanics and Engineering 1996; 134:71-90.
29. Shakib F, Hughes TJR. A new finite element formulation for computational fluid dynamics: IX. Fourier analysis of space-time Galerkin/least-squares algorithms. Computer Methods in Applied Mechanics and Engineering 1991; 87:35-58.
30. Johnson C. Discontinuous Galerkin finite element methods for second order hyperbolic problems. Computer Methods in Applied Mechanics and Engineering 1993; 107:117-129.
31. Aziz AK, Monk P. Continuous finite elements in space and time for the heat equation. Mathematics of Computation 1998; 144:70-97.
32. French DA. A space-time finite element method for the wave equation. Computer Methods in Applied Mechanics and Engineering 1993; 107:145-157.
33. French DA, Peterson TE. A continuous space-time finite element method for the wave equation. Mathematics of Computation 1996; 65:491-506.
34. Hulme BL. Discrete Galerkin and related one-step methods for ordinary differential equations. Mathematics of Computation 1972; 26-120:881-891.
35. Jamet P. Stability and convergence of a generalized Crank-Nicolson scheme on a variable mesh for the heat equation. SIAM Journal on Numerical Analysis 1980; 17(4):530-539.