Refinement Indicator for Mesh Adaption in Shallow-Water Modeling
Publication: Journal of Hydraulic Engineering
Volume 132, Issue 8
Abstract
Automatic mesh refinement can create suitable resolution for a hydrodynamic simulation in a computationally efficient manner. Development of an automatic adaptive procedure will rely on estimating and/or controlling computational error by adapting the mesh parameters with respect to a particular measurement. Since a primary source of error in a discrete approximation of the shallow-water equations is inadequate mesh resolution, an adaptive mesh can be an efficient approach to increase accuracy. This paper introduces a simple indicator for the shallow water equations that measures the error in a norm of mass conservation to determine which elements require refinement or coarsening. The resulting adaptive grid gives results comparable to a much higher resolution (uniformly refined) mesh with less computational expense.
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Acknowledgments
The experiments described and the results presented were obtained from research sponsored by the Navigation Systems Research Program and the System-Wide Water Resources Program by the U.S. Army Engineer Research and Development Center, Coastal and Hydraulics Laboratory. Permission was granted by the Chief of Engineers to publish this information.
References
Babuška, I., Strouboulis, T., Upadhyay, C. S., and Gangaraj, S. K. (1995). “A posteriori estimation and adaptive control of the pollution error in the -version of the finite-element method.” Int. J. Numer. Methods Eng., 38, 4207–4235.
Berger, R. C., and Howington, S. E. (2002). “Discrete fluxes and mass balance in finite elements.” J. Hydraul. Eng., 128(1), 87–92.
Berger, R. C., and Stockstill, R. L. (1995). “Finite-element model for high-velocity channels.” J. Hydraul. Eng., 121(10), 710–716.
Cecchi, M. M., and Marcuzzi, F. (1999). “Adaptivity in space and time for shallow water equations.” Int. J. Numer. Methods Fluids, 31, 285–297.
Hensley, J. (2003). “Use of adaptive meshes in ADH for flow problems.” Proc., HPC Users Group Conf., Belluve, Wash.
Hughes, T. J. R., Engel, G., Mazzei, L., and Larson, M. G. (2000). “The continuous Galerkin method is locally conservative.” J. Comput. Phys., 163(2), 467–488.
Prudhomme, S. M. (1999). “Adaptive control of error and stability of h-p approximations of the transient Navier-Stokes equations.” Ph.D. thesis, Univ. of Texas at Austin, Austin, Tex.
Prudhomme, S., and Oden, J. T. (2002). “Numerical stability and error analysis for the incompressible Navier-Stokes equations.” Commun. Numer. Methods Eng., 18, 779–787.
Information & Authors
Information
Published In
Journal of Hydraulic Engineering
Volume 132 • Issue 8 • August 2006
Pages: 854 - 857
Copyright
© 2006 ASCE.
History
Received: Mar 1, 2005
Accepted: Aug 19, 2005
Published online: Aug 1, 2006
Published in print: Aug 2006
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