Automatic, unstructured mesh generation for tidal calculations in a large domain

An automated procedure is described for the production of unstructured, finite element meshes to perform depth-integrated, hydrodynamic calculations in an ocean-scale, two-dimensional domain. Three relatively coarse meshes with nearly identical boundaries are automatically produced by basing internal size guidelines on a localized truncation error analysis that was performed using results from a highly resolved mesh. Qualitative and quantitative comparisons of model performance are made at 150 historical tidal stations. The coarsest mesh is shown to meet or exceed the overall accuracy of the other meshes, including a highly resolved mesh that has over six times as many computational points. The automated procedure quickly and easily produces a computationally efficient and accurate finite element mesh that is reproducible. In addition, the methodology is shown to have potential for assessing the importance and accuracy of and bathymetric details and evaluating historical hydrodynamic data.

[1]  R. Luettich,et al.  Modelling tides in the western North Atlantic using unstructured graded grids , 1994 .

[2]  S. K. Runcorn International dictionary of geophysics : seismology, geomagnetism, aeronomy, oceanography, geodesy, gravity, marine geophysics, meteorology, the earth as a planet and its evolution , 1967 .

[3]  John M. Sullivan,et al.  Adaptive mesh generation using a normal offsetting technique , 1997 .

[4]  Joannes J. Westerink,et al.  Aspects of nonlinear simulations using shallow-water models based on the wave continuity equation , 1994 .

[5]  Joannes J. Westerink,et al.  Two-dimensional, unstructured mesh generation for tidal models , 2001 .

[6]  John D. Wang Real-Time Flow in Unstratified Shallow Water , 1978 .

[7]  R. L. Bates,et al.  Glossary of Geology , 1987 .

[8]  S. N. Muthukrishnan,et al.  Topological refinement procedures for triangular finite element meshes , 1996, Engineering with Computers.

[9]  R. Löhner,et al.  Progress in grid generation via the advancing front technique , 2005, Engineering with Computers.

[10]  Joannes J. Westerink,et al.  General Spectral Computations of the Nonlinear Shallow Water Tidal Interactions within the Bight of Abaco , 1989 .

[11]  P. Guyenne,et al.  International Journal for Numerical Methods in Fluids a Fully Non-linear Model for Three-dimensional Overturning Waves over an Arbitrary Bottom , 2009 .

[12]  C. Provost,et al.  A hydrodynamic ocean tide model improved by assimilating a satellite altimeter-derived data set , 1998 .

[13]  Paul-Louis George,et al.  The advancing-front mesh generation method revisited , 1994 .

[14]  S. Hagen,et al.  Meshing Requirements for Tidal Modeling in the Western North Atlantic , 2004 .

[15]  André B. Fortunato,et al.  Tidally generated shelf waves off the western Iberian coast , 2002 .

[16]  J. Westerink,et al.  International Journal for Numerical Methods in Fluids One-dimensional Finite Element Grids Based on a Localized Truncation Error Analysis , 2022 .

[17]  Roy A. Walters,et al.  Accuracy of an estuarine hydrodynamic model using smooth elements , 1980 .

[18]  J. Sullivan,et al.  Fully automatic two dimensional mesh generation using normal offsetting , 1992 .

[19]  Ingemar Kinnmark,et al.  The Shallow Water Wave Equations: Formulation, Analysis and Application , 1985 .

[20]  William G. Gray,et al.  A wave equation model for finite element tidal computations , 1979 .

[21]  Norman W. Scheffner,et al.  ADCIRC: An Advanced Three-Dimensional Circulation Model for Shelves, Coasts, and Estuaries. Report 1. Theory and Methodology of ADCIRC-2DDI and ADCIRC-3DL. , 1992 .

[22]  William G. Gray,et al.  Progress in Surface Water Modeling , 1991 .

[23]  W. G. Gray,et al.  Shallow water modeling in spherical coordinates: equation formulation, numerical implementation, and application , 1994 .

[24]  David G. Aubrey,et al.  A study of non-linear tidal propagation in shallow inlet/estuarine systems Part II: Theory☆ , 1985 .

[25]  John David Howlett Size Function Based Mesh Relaxation , 2005 .

[26]  P. George,et al.  Automatic mesh generator with specified boundary , 1991 .

[27]  Scott C. Hagen,et al.  Estimation of the Truncation Error for the Linearized, Shallow Water Momentum Equations , 2001, Engineering with Computers.