Accès libre

Lagrange–Galerkin methods for the incompressible Navier-Stokes equations: a review

Communications in Applied and Industrial Mathematics's Cover Image
Communications in Applied and Industrial Mathematics
"Special Issue on New Trends in Semi-Lagrangian Methods, Guest Editors: Luca Bonaventura, Maurizio Falcone and Roberto Ferretti
À propos de cet article

Citez

1. Y. Achdou, J.-L.Guermond, Convergence analysis of a finite element projection/Lagrange-Galerkin method for the incompressible Navier-Stokes equations, SIAM Journal on Numerical Analysis, vol. 37, pp. 799-826, 2000.10.1137/S0036142996313580Search in Google Scholar

2. A. Allievi, R. Bermejo, A generalized particle search-locate algorithm for arbitrary grids, Journal of Computational Physics, vol. 132, pp.157166, 1997.Search in Google Scholar

3. R. Bermejo, L. Saavedra, A second order in time local projection stabilized Lagrange-Galerkin method for Navier-Stokes equations at high Reynolds numbers, Computers and Mathematics with Applications, to appear, 2015.10.1007/978-3-319-32013-7_24Search in Google Scholar

4. R. Bermejo, L. Saavedra, Modified Lagrange-Galerkin methods to integrate time dependent incompressible Navier-Stokes equations, SIAM Journal on Scietific Computing, to appear, 2015.10.1137/140973967Search in Google Scholar

5. R. Bermejo, P. Galfian del Sastre and L. Saavedra, A second order in time modified Lagrange-Galerkin finite element method for the incompressible Navier-Stokes equations, SIAM Journal on Numerical Analysis, vol.50, pp. 3084-3109, 2012.Search in Google Scholar

6. R. Bermejo and L. Saavedra, Modified Lagrange-Galerkin methods of first and second order in time for convection-diffusion problems, Numerische Mathematik, vol. 120, pp. 601-638, 2012.10.1007/s00211-011-0418-8Search in Google Scholar

7. K. Boukir, Y. Maday, B. Mfietivet and E. Razanfindrakoto, A high-order characteristics/finite element method for the incompressible Navier Stokes equations, International Journal on Numerical Methods in Fluids, vol. 25, pp. 1421-1454, 1997.Search in Google Scholar

8. M. Braack and T. Richter, Solutions of 3D Navier-Stokes benchmark problems with adaptive finite elements, Computers and Fluids, vol. 35, pp. 372-392, 2006.10.1016/j.compfluid.2005.02.001Search in Google Scholar

9. G.C. Buscaglia, A. Dari, Implementation of the Lagrange-Galerkin method for the incompressible Navier-Stokes equations, International Journal of Numerical Methods in Fluids, vol. 15, pp. 23-36, 199210.1002/fld.1650150103Search in Google Scholar

10. J. Douglas and T.F. Russell, Numerical methods for convection50 dominated diffusion problems based on combining the method of characteristics with finite element or finite difference procedures, SIAM Journal on Numerical Analysis, vol. 19, pp. 871-885, 1982.10.1137/0719063Search in Google Scholar

11. M. El-Amrani, M. Seaid, An L2-projection for the GalerkinCharacteristic solution for incompressible ows, SIAM Journal on Scientific Computing, vol. 33, pp. 3110-3131, 2011.Search in Google Scholar

12. P. Galán del Sastre, R. Bermejo, A comparison of semi-Lagrangian and Lagrange-Galerkin hp-FEM methods in convection-diffusion problems, Communications in Computational Physics, vol. 9, pp. 1020-1039, 2011.Search in Google Scholar

13. J.-L. Guermond, P. Minev, Analysis of a projection/characteristic scheme for incompressible ow, Communications in Numerical Methods in Engineering, vol. 19, pp. 535-550, 2003.10.1002/cnm.611Search in Google Scholar

14. J.-L. Guermond, P.Minev, J. Shen, Error analysis of pressure-correction schemes for the Navier-Stokes equations with open boundary conditions, SIAM Journal on Numerical Analysis, vol. 43, pp. 239-258, 2005.10.1137/040604418Search in Google Scholar

15. J.-L. Guermond, J. Shen, On the error estimates for the rotational pressure-correction projection methods, Mathematics of Computation, vol 73 (248), pp. 1719-1737, 2004.Search in Google Scholar

16. E. Hachem, B. Rivaux, T. Kloczko, H. Digonnet and T. Coupez. Stabilized finite element method for incompressible flows with high Reynolds number, Journal of Computational Physics, vol. 229, pp. 8643-8665, 2010.Search in Google Scholar

17. V. John. Higher order finite element methods and multigrid solvers in a benchmark problem for the 3D Navier-Stokes equations, International Journal of Numerical Methods in Fluids, vol. 40, pp. 775-798, 2002.10.1002/fld.377Search in Google Scholar

18. H. C. Ku, R. S. Hirsh and T. D. Taylor. A pseudospectral method for solution of the three-dimensional incompressible Navier-Stokes equations, Journal of Computational. Physics, vol. 70, pp. 439-462, 1987.10.1016/0021-9991(87)90190-2Search in Google Scholar

19. P.D. Minev, C.R. Ethier, A characteristic/finite element algorithm for the 3D Navier-Stokes equations using unstructured grids, Computer Methods in Applied Mechanics and Engineering, vol. 178, pp. 39-50, 1999.10.1016/S0045-7825(99)00003-1Search in Google Scholar

20. K. W. Morton, A. Priestley and E. Süli, Stability of the Lagrange-Galerkin method with non-exact integration, M2AN Mathematical Modelling and Numerical Analysis, vol. 22, pp. 625-653, 1988.10.1051/m2an/1988220406251Search in Google Scholar

21. H. Notsu and M. Tabata, A single-step characteristic-curve finite element scheme of second order in time for the incompresible Navier-Stokes equations, Journal of Scientific Computing, vol. 38, pp. 1-14, 2009.10.1007/s10915-008-9217-5Search in Google Scholar

22. A. Priestley, Exact projections and the Lagrange-Galerkin method: a realistic alternative to quadrature, Journal of Computational Physics, vol. 112, pp. 316-333, 199410.1006/jcph.1994.1104Search in Google Scholar

23. O. Pironneau, On the transport-diffusion algorithm and its applications to the Navier-Stokes equations, Numerische Mathematik, vol. 38, pp. 309-332, 1982.10.1007/BF01396435Search in Google Scholar

24. H.-G. Roos, M. Stynes, Robuts Numerical Methods for Singularly Perturbed Difierential Equations, Springer Series in Computational Mathematics, Springer-Verlag, Berlin, 2008.Search in Google Scholar

25. M. Schäfer and S. Turek, Benchmark computations of laminar ow around a cylinder (With support by Durst F, Krause E, Rannacher R). In: Schäfer E, editor. Flow simulation with high-performance computers II. DFG priority research program results 1993-1995. Notes numer. fluid mech, no. 52. Wiesbaden Vieweg; 547-566, 1996.10.1007/978-3-322-89849-4_39Search in Google Scholar

26. C. Shu, L. Wang and Y. T. Chew Numerical computation of three dimensional incompressible Navier-Stokes equations in primitive variable form by DQ method, International Journal for Numerical Methods in Fluids, vol.43, pp. 345-368, 2003.10.1002/fld.566Search in Google Scholar

27. E. Süli, Convergence and nonlinear stability of the Lagrange-Galerkin method for the Navier-Stokes equations, Numerische Mathematik, vol.54, pp. 459-483, 1988.10.1007/BF01396329Search in Google Scholar

28. L.Q. Tang, T. Cheng and T.T.H. Tsang Transient solutions for three dimensional lid-driven cavity flows by a least-squares finite element method, International Journal for Numerical Methods in Fluids, vol. 21, pp. 413-432, 1995.10.1002/fld.1650210505Search in Google Scholar

29. C. Temperton, A. Staniforth, An eficient two-time-level semi Lagrangian semi-implicit integration scheme, Quaterly Journal of the Royal Meteorological Society, vol. 113, pp. 1025-1039, 1987.Search in Google Scholar

30. D.Xiu and G.E.Karniadakis, A semi-Lagrangian high order method for Navier-Stokes equations, Journal of Computational Physics, vol.172, pp. 658-684, 2001.10.1006/jcph.2001.6847Search in Google Scholar

eISSN:
2038-0909
Langue:
Anglais
Périodicité:
Volume Open
Sujets de la revue:
Mathematics, Numerical and Computational Mathematics, Applied Mathematics