- About this Journal ·
- Abstracting and Indexing ·
- Aims and Scope ·
- Annual Issues ·
- Article Processing Charges ·
- Articles in Press ·
- Author Guidelines ·
- Bibliographic Information ·
- Citations to this Journal ·
- Contact Information ·
- Editorial Board ·
- Editorial Workflow ·
- Free eTOC Alerts ·
- Publication Ethics ·
- Reviewers Acknowledgment ·
- Submit a Manuscript ·
- Subscription Information ·
- Table of Contents
Abstract and Applied Analysis
Volume 2013 (2013), Article ID 161873, 13 pages
A Pressure-Stabilized Lagrange-Galerkin Method in a Parallel Domain Decomposition System
School of Engineering, Sun Yat-Sen University, 510275 Guangzhou, China
Received 30 April 2013; Accepted 14 June 2013
Academic Editor: Santanu Saha Ray
Copyright © 2013 Qinghe Yao and Qingyong Zhu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
- M. Bercovier, O. Pironneau, and V. Sastri, “Finite elements and characteristics for some parabolic-hyperbolic problems,” Applied Mathematical Modelling, vol. 7, no. 2, pp. 89–96, 1983.
- J. Douglas Jr. and T. F. Russell, “Numerical methods for convection-dominated diffusion problems based on combining the method of characteristics with finite element or finite difference procedures,” SIAM Journal on Numerical Analysis, vol. 19, no. 5, pp. 871–885, 1982.
- O. Pironneau, “On the transport-diffusion algorithm and its applications to the Navier-Stokes equations,” Numerische Mathematik, vol. 38, no. 3, pp. 309–332, 1982.
- T. F. Russell, “Time stepping along characteristics with incomplete iteration for a Galerkin approximation of miscible displacement in porous media,” SIAM Journal on Numerical Analysis, vol. 22, no. 5, pp. 970–1013, 1985.
- O. Pironneau, Finite Element Methods for Fluids, John Wiley & Sons, Chichester, UK, 1989.
- H. Notsu, “Numerical computations of cavity flow problems by a pressure stabilized characteristic-curve finite element scheme,” in Japan Society for Computational Engineering and Science, 2008.
- H. Notsu and M. Tabata, “A combined finite element scheme with a pressure stabilization and a characteristic-curve method for the Navier-Stokes equations,” Transactions of the Japan Society for Industrial and Applied Mathematics, vol. 18, no. 3, pp. 427–445, 2008.
- M. Tabata and S. Fujima, “Robustness of a characteristic finite element scheme of second order in time increment,” in Computational Fluid Dynamics 2004, pp. 177–182, 2006.
- H. Rui and M. Tabata, “A second order characteristic finite element scheme for convection-diffusion problems,” Numerische Mathematik, vol. 92, no. 1, pp. 161–177, 2002.
- N. Massarotti, P. Nithiarasu, and O. C. Zienkiewicz, “Characteristic-based split (CBS) algorithm for incompressible flow problems with heat transfer,” International Journal of Numerical Methods for Heat and Fluid Flow, vol. 11, no. 3, p. 278, 2001.
- F. Brezzi and M. Fortin, Mixed and Hybrid Finite Element Methods, vol. 15 of Springer Series in Computational Mathematics, Springer, New York, NY, USA, 1991.
- F. Brezzi and J. Douglas Jr., “Stabilized mixed methods for the Stokes problem,” Numerische Mathematik, vol. 53, no. 1-2, pp. 225–235, 1988.
- H. Jia, D. Liu, and K. Li, “A characteristic stabilized finite element method for the non-stationary Navier-Stokes equations,” Computing, vol. 93, no. 1, pp. 65–87, 2011.
- H. Kanayama, D. Tagami, T. Araki, and H. Kume, “A stabilization technique for steady flow problems,” International Journal of Computational Fluid Dynamics, vol. 18, no. 4, pp. 297–301, 2004.
- C. R. Dohrmann and P. B. Bochev, “A stabilized finite element method for the Stokes problem based on polynomial pressure projections,” International Journal for Numerical Methods in Fluids, vol. 46, no. 2, pp. 183–201, 2004.
- H. M. Park and M. C. Sung, “Stabilization of two-dimensional Rayleigh-Bénard convection by means of optimal feedback control,” Physica D, vol. 186, no. 3-4, pp. 185–204, 2003.
- T. Barth, P. Bochev, M. Gunzburger, and J. Shadid, “A taxonomy of consistently stabilized finite element methods for the Stokes problem,” SIAM Journal on Scientific Computing, vol. 25, no. 5, pp. 1585–1607, 2004.
- P. B. Bochev, M. D. Gunzburger, and R. B. Lehoucq, “On stabilized finite element methods for the Stokes problem in the small time step limit,” International Journal for Numerical Methods in Fluids, vol. 53, no. 4, pp. 573–597, 2007.
- G. C. Buscaglia and E. A. Dari, “Implementation of the Lagrange-Galerkin method for the incompressible Navier-Stokes equations,” International Journal for Numerical Methods in Fluids, vol. 15, no. 1, pp. 23–26, 1992.
- H. A. van der Vorst, Iterative Krylov Methods for Large Linear Systems, vol. 13 of Cambridge Monographs on Applied and Computational Mathematics, Cambridge University Press, Cambridge, UK, 2003.
- T. J. R. Hughes, L. P. Franca, and M. Balestra, “A new finite element formulation for computational fluid dynamics. V. Circumventing the Babuška-Brezzi condition: a stable Petrov-Galerkin formulation of the Stokes problem accommodating equal-order interpolations,” Computer Methods in Applied Mechanics and Engineering, vol. 59, no. 1, pp. 85–99, 1986.
- A. Toselli and O. Widlund, Domain Decomposition Methods—Algorithms and Theory, vol. 34 of Springer Series in Computational Mathematics, Springer, Berlin, Germany, 2005.
- Q. Yao, H. Kanayama, H. Notsu, and M. Ogino, “Balancing domain decomposition for non-stationary incompressible flow problems using a characteristic-curve method,” Journal of Computational Science and Technology, vol. 4, pp. 121–135, 2010.
- Q. H. Yao and Q. Y. Zhu, “Investigation of the contamination control in a cleaning room with a moving Agv by 3D large-scale simulation,” Journal of Applied Mathematics, vol. 2013, Article ID 570237, 10 pages, 2013.
- “Adventure Project,” http://adventure.sys.t.u-tokyo.ac.jp/.
- C. W. Hall, Laws and Models: Science, Engineering, and Technology, CRC Press, 2000.
- R. S. Brodkey and H. C. Hershey, Basic Concepts in Transport Phenomena, Brodkey, 2001.
- S. M. Richardson, Fluid Mechanics, Hemisphere, 1989.
- 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, no. 23, pp. 8643–8665, 2010.
- M. T. Manzari, “An explicit finite element algorithm for convection heat transfer problems,” International Journal of Numerical Methods for Heat and Fluid Flow, vol. 9, no. 8, pp. 860–877, 1999.
- N. A. Malamataris, “A numerical investigation of wall effects in three-dimensional, laminar flow over a backward facing step with a constant aspect and expansion ratio,” International Journal for Numerical Methods in Fluids, vol. 71, pp. 1073–1102, 2013.
- P. T. Williams and A. J. Baker, “Numerical simulations of laminar flow over a 3D backward-facing step,” International Journal for Numerical Methods in Fluids, vol. 24, no. 11, pp. 1159–1183, 1997.
- H. Kanayama, K. Komori, and D. Sato, “Development of a Thermal Convection Solver with Hierarchical Domain Decomposition Method,” in Proceedings of the 8th World Congress on Computational Mechanics and the 5th European Congress on Computational Methods in Applied Sciences and Engineering, Venice, Italy, 2008.
- K. L. Wong and A. J. Baker, “A 3D incompressible Navier-Stokes velocity-vorticity weak form finite element algorithm,” International Journal for Numerical Methods in Fluids, vol. 38, no. 2, pp. 99–123, 2002.
- G. de Vahl Davis, “Natural convection of air in a square cavity: a bench mark numerical solution,” International Journal for Numerical Methods in Fluids, vol. 3, no. 3, pp. 249–264, 1983.
- G. de Vahl Davis and I. P. Jones, “Natural convection in square cavity: a comparison exercise,” International Journal for Numerical Methods in Fluids, vol. 3, no. 3, pp. 227–248, 1983.