Energy stable and momentum conserving hybrid finite element method for the incompressible Navier-Stokes equations

SIAM Journal on Scientific Computing

Volumn 34, Issue 2, 2012, Pages

  Labeur, Robert Jan ^a   Wells, Garth N ^b  

^a DELFT UNIVERSITY OF TECHNOLOGY   (Netherlands)

^b UNIVERSITY OF CAMBRIDGE   (United Kingdom)

Author keywords

Finite element method; Hybrid finite element methods; Incompressible Navier Stokes equations

Indexed keywords

CONSTRAINED OPTIMIZATION; DEGREES OF FREEDOM (MECHANICS); FINITE ELEMENT METHOD; GALERKIN METHODS; MOMENTUM; NAVIER STOKES EQUATIONS; TRANSPIRATION; VELOCITY; VISCOUS FLOW;

ENERGY; ENERGY STABILITY; GLOBAL ENERGY; HYBRID FINITE ELEMENT METHODS; INCOMPRESSIBLE (NAVIER )STOKES EQUATION; INCOMPRESSIBLE NAVIER STOKES EQUATIONS; MASS CONSERVATION; MOMENTUM CONSERVATIONS; PRESSURE-FIELD; VELOCITY FIELD;

LAGRANGE MULTIPLIERS;

EID: 84861356260     PISSN: 10648275     EISSN: None     Source Type: Journal    
DOI: 10.1137/100818583     Document Type: Article

References (27)

1. B. F. Armaly, F. Durst, J. C. F. Pereira, and B. Schönung, Experimental and theoretical investigation of backward-facing step flow, J. Fluid Mech., 127 (1983), pp. 473-496. (Pubitemid 13504335)
2. D. N. Arnold, F. Brezzi, B. Cockburn, and L. D. Marini, Unified analysis of discontinuous Galerkin methods for elliptic problems, SIAM J. Numer. Anal., 39 (2002), pp. 1749-1779.
3. B. Cockburn, B. Dong, J. Guzmán, M. Restelli, and R. Sacco, A hybridizable discontinuous Galerkin method for steady-state convection- diffusion-reaction problems, SIAMJ. Sci. Comput., 31 (2009), pp. 3827-3846.
4. B. Cockburn, J. Gopalakrishnan, and R. Lazarov, Unified hybridization of discontinuous Galerkin, mixed, and continuous Galerkin methods for second order elliptic problems, SIAM J. Numer. Anal., 47 (2009), pp. 1319-1365.
5. B. Cockburn, G. Kanschat, and Schötzau, An equal-order DG method for the incompressible Navier-Stokes equations, J. Sci. Comput., 40 (2009), pp. 188-210.
6. B. Cockburn, G. Kanschat, D. Schötzau, and Ch. Schwab, Local discontinuous Galerkin methods for the Stokes system, SIAM J. Numer. Anal., 40 (2002), pp. 319-343.
7. H. Egger and J. Schöberl, A hybrid mixed discontinuous Galerkin finite-element method for convection-diffusion problems, IMA J. Numer. Anal., 30 (2010), pp. 1206-1234.
8. H. C. Elman, D. J. Silvester, and A. J. Wathen, Finite Elements and Fast Iterative Solvers with Applications in Incompressible Fluid Dynamics, Oxford University Press, Oxford, 2005.
9. P. M. Gresho, R. L. Sani, and M. S. Engelman, Incompressible Flow and the Finite Element Method, John Wiley and Sons, Chichester, UK, 1998.
10. S. Güzey, B. Cockburn, and H. K. Stolarski, The embedded discontinuous Galerkin method: Application to linear shell problems, Internat. J. Numer. Methods Engrg., 70 (2007), pp. 757-790. (Pubitemid 46804272)
11. P. Hansbo and M. G. Larson, Discontinuous Galerkin methods for incompressible and nearly incompressible elasticity by Nitsche's method, Comput. Methods Appl. Mech. Engrg., 191 (2002), pp. 1895-1908. (Pubitemid 34231765)
12. T. J. R. Hughes and L. P. Franca, A new finite element formulation for computational fluid dynamics: VII. The Stokes problem with various well-posed boundary conditions: Symmetric formulations that converge for all velocity/pressure spaces, Comput. Methods Appl. Mech. Engrg., 65 (1987), pp. 85-96.
13. T. J. R. Hughes, G. Scovazzi, P. B. Bochev, and A. Buffa, A multiscale discontinuous Galerkin method with the computational structure of a continuous Galerkin method, Comput. Methods Appl. Mech. Engrg., 195 (2006), pp. 2761-2787.
14. T. J. R. Hughes and G. N. Wells, Conservation properties for the Galerkin and stabilised forms of the advection-diffusion and incompressible Navier-Stokes equations, Comput. Methods Appl. Mech. Engrg., 194 (2005), pp. 1141-1159. (Pubitemid 40133564)
15. J. Kim and P. Moin, Application of a fractional-step method to incompressible Navier-Stokes equations, J. Comput. Phys., 59 (1985), pp. 308-323.
16. R. C. Kirby and A. Logg, A compiler for variational forms, ACM Trans. Math. Software, 32 (2006), pp. 417-444. (Pubitemid 44495249)
17. R. M. Kirby and J. S. Spencer, Stabilization of spectral/hp element methods through spectral vanishing viscosity: Application to fluid mechanics modelling, Comput. Methods Appl. Mech. Engrg., 195 (2006), pp. 3128-3144.
18. L. Kovasznay, Laminar flow behind a two-dimensional grid, Proc. Cambridge Philos. Soc., 44 (1948), pp. 58-62.
19. R. J. Labeur and G. N. Wells, A Galerkin interface stabilisation method for the advectiondiffusion and incompressible Navier-Stokes equations, Comput. Methods Appl. Mech. Engrg., 196 (2007), pp. 4985-5000. (Pubitemid 47423965)
20. R. J. Labeur and G. N. Wells, Interface stabilised finite element method for moving domains and free-surface flows, Comput. Methods Appl. Mech. Engrg., 198 (2009), pp. 615-630.
21. R. J. Labeur and G. N. Wells, Supporting Material, 2012; available online from http://www. dspace.cam.ac.uk/handle/1810/241077.
22. A. Logg and G. N. Wells, DOLFIN: Automated finite element computing, ACM Trans. Math. Software, 37 (2010), pp. 20:1-20:28.
23. N. C. Nguyen, J. Peraire, and B. Cockburn, A hybridizable discontinuous Galerkin method for Stokes flow, Comput. Methods Appl. Mech. Engrg., 199 (2010), pp. 582-597.
24. K. B. Ølgaard, A. Logg, and G. N. Wells, Automated code generation for discontinuous Galerkin methods, SIAM J. Sci. Comput., 31 (2008), pp. 849-864.
25. K. B. Ølgaard and G. N. Wells, Optimisations for quadrature representations of finite element tensors through automated code generation, ACM Trans. Math. Software, 37 (2010), pp. 8:1-8:23.
26. T. Warburton, L. F. Pavarino, and J. S. Hesthaven, A pseudo-spectral scheme for the incompressible Navier-Stokes equations using unstructured nodal elements, J. Comput. Phys., 164 (2000), pp. 1-21.
27. G. N. Wells, Analysis of an interface stabilized finite element method: The advectiondiffusion- reaction equation, SIAM J. Numer. Anal., 49 (2011), pp. 87-109.