CFP last date
20 January 2025
Call for Paper
February Edition
IJCA solicits high quality original research papers for the upcoming February edition of the journal. The last date of research paper submission is 20 January 2025

Submit your paper
Know more
The week's pick
Responsive image
SFLA-Based Line Balancing and Task Optimization in Master-Slave Controlled Hanger Transportation Systems for Garment Production

Duc Hoang Nguyen
Random Articles
Reseach Article

A High-Order Nodal Discontinuous Galerkin Method for 1D Morphodynamic Modelling

by Nouh Izem, Mohammed Seaid, Mohamed Wakrim
journal cover thumbnail

International Journal of Computer Applications
Foundation of Computer Science (FCS), NY, USA
Volume 41 - Number 15
Year of Publication: 2012
Authors: Nouh Izem, Mohammed Seaid, Mohamed Wakrim
10.5120/5616-7895

Nouh Izem, Mohammed Seaid, Mohamed Wakrim . A High-Order Nodal Discontinuous Galerkin Method for 1D Morphodynamic Modelling. International Journal of Computer Applications. 41, 15 ( March 2012), 19-27. DOI=10.5120/5616-7895

@article{ 10.5120/5616-7895,
author = { Nouh Izem, Mohammed Seaid, Mohamed Wakrim },
title = { A High-Order Nodal Discontinuous Galerkin Method for 1D Morphodynamic Modelling },
journal = { International Journal of Computer Applications },
issue_date = { March 2012 },
volume = { 41 },
number = { 15 },
month = { March },
year = { 2012 },
issn = { 0975-8887 },
pages = { 19-27 },
numpages = {9},
url = { https://ijcaonline.org/archives/volume41/number15/5616-7895/ },
doi = { 10.5120/5616-7895 },
publisher = {Foundation of Computer Science (FCS), NY, USA},
address = {New York, USA}
}
%0 Journal Article
%1 2024-02-06T20:29:40.113256+05:30
%A Nouh Izem
%A Mohammed Seaid
%A Mohamed Wakrim
%T A High-Order Nodal Discontinuous Galerkin Method for 1D Morphodynamic Modelling
%J International Journal of Computer Applications
%@ 0975-8887
%V 41
%N 15
%P 19-27
%D 2012
%I Foundation of Computer Science (FCS), NY, USA
Abstract

In this paper we present a numerical solution of the sediment transport equations in one horizontal dimension, based on a discontinuous Galerkin finite-element method. The continuous equations are discretized using nodal polynomial basis functions of arbitrary order in space on each element of an unstructured computational domain. To complete the discretization in space, we choose the numerical flux based in the local Lax-Friedrichs flux. A third-order explicit Runge-Kutta scheme is used to advance the solution in time. In spite of the local time steps the scheme is locally conservative, fully explicit, and arbitrary order accurate in space and time for transient calculations. Numerical results are shown for the one-dimensional with orders of accuracy two up to six in space.

References
  1. Grass AJ. Sediment transport by waves and currents. SERC London Cent. Mar. Technol. Report No: FL29, 1981.
  2. Y. Bazilevs and TJR. Hughes. Weak imposition of dirichlet boundary conditions in fluid mechanics. Computers & Fluids, in press, 36:12–26, 2007.
  3. Bernini A. Caleffi V, Valiani A. High-order balanced cweno scheme for movable bed shallow water equations. Advances in Water Resources, 30:730–741, 2007.
  4. B. Cockburn, G. E. Karniadakis, and C. -W. Shu (eds. ). Discontinuous Galerkin methods. Theory, computation and applications. Lecture Notes in Computational Science and Engineering, 11. Springer-Verlag, Berlin, 2000.
  5. Holz K. P. Crotogino A. Numerical movable-bed models for practical engineering. Applied Mathematical Modelling, 8:45–49, 1984.
  6. Papoglou I. DelisA. I. Relaxation approximation to bed-load sediment transport. J. Comput. Appl. Math. , 213:521–546, 2008.
  7. M. Seaid, F. Benkhaldoun, S. Sahmim. "Solution of the sediment transport equations using a finite volume method based on sign matrix". SIAM J. Sci. Comp, Vol. 31, No. 4:2866–2889, 2009.
  8. M. Seaid, F. Benkhaldoun, S. Sahmim. Mathematical development and verification of a finite volume model for morphodynamic flow applications. accepted in Advances in Applied Mathematics and Mechanics, 2011.
  9. S. Gottlieb, C. W. Shu, and E. Tadmor. Strong stability preserving high order time integration methods. SIAM Rev. , 43:89–112, 2001.
  10. J. S. Hesthaven and T. Warburton. High-order nodal methods on unstructured grids. I. time-domain solution of maxwells equations. J Comp Phys, 181(1):186–221, 2002.
  11. J. Hudson. Numerical techniques for morphodynamic modelling. Ph. D. Thesis, University of Reading, 2001.
  12. Sweby P. K. Hudson, J. Formulations for numerically approximating hyperbolic systems governing sediment transport. J. Sci. Comput. , 19:225–252, 2003.
  13. TJR. Hughes, G. Scovazzi, PB. Bochev, and A. Buffa. A multiscale discontin- uous Galerkin method with the computational structure of a continuous Galerkin method. Computer Methods in Applied Mechanics and Engineering, 195:2761–2787, 2006.
  14. N. Dodd T. Chesher A. Cooper J. Hudson, J. Damgaard. Numerical approaches for 1d morphodynamic modelling. Coastal Eng. , 52:691–707, 2005.
  15. C. W. Shu J. Qiu, B. C. Khoo. A numerical study for the performance of the rungekutta discontinuous galerkin method based on different numerical fluxes. J. Comput. Phys. , 212:540–565, 2006.
  16. A. Verway J. A. Cunge, F. M. Holly. Practical Aspects of Computational River Hy- draulics. Pitman, London, 1980.
  17. R. J. Leveque. Finite Volume Methods for Hyperbolic Problems. Cambridge Univer- sity Press, Cambridge, 2002.
  18. Shao Z. Long W, Kirby J. T. A numerical scheme for morphological bed level calculations. Coastal Engineering, 55:167–180, 2008.
  19. L. Sopta N. Crnjaric-Zic, S. Vukovic. Extension of eno and weno schemes to one-dimensional sediment transport equations. Comput. Fluids, 33:31–56, 2004.
  20. Roe P. L. Approximate riemann solvers, parameter vectors and difference schemes. J. Comp. Physics. , 43:357–372, 1981.
  21. Hogg A. J. Pritchard D. On sediment transport under dam-break flow. J. FluidMech. , 473:265–274, 2002.
  22. Fraccarollo L. Rosatti G. A well-balanced approach for flows over mobile-bed with high sediment-transport. J. Comput. Physics, 220:312–338, 2006.
  23. C. W. Shu. Total variation diminishing time discretizations. SIAM J. Sci. Stat. Comput. , 9:1073–1084, 1988.
Index Terms

Computer Science
Information Sciences

Keywords

Morphodynamic Model Discontinuous Galerkin Finite-element Method Shallow Water Equations Sediment Transport

Powered by PhDFocusTM