Volume 3, Issue 1
A Transformed Coordinates Shallow Water Model for the Head of the Bay of Bengal Using Boundary-Fitted Curvilinear Grids

Farzana Hussain

East Asian J. Appl. Math., 3 (2013), pp. 27-47.

Published online: 2018-02

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  • Abstract

The Bay of Bengal is surrounded by coastline except to the south, where there is open sea. The coastline bends most sharply along the coast of Bangladesh, and there are many small and large islands in the offshore region there. In order to incorporate the island boundaries and the curved coastline properly, in any numerical scheme it is often necessary to consider a very fine grid resolution along the coastal belts whereas this is unnecessary away from the coasts. However, a very fine resolution involves more memory and more CPU time in the numerical solution process, and invites numerical instability. On the other hand, boundary-fitted curvilinear grids in hydrodynamic models for coastal seas, bays and estuaries not only fit to the coastline but also render the finite difference schemes simpler and more accurate. In this article, the boundary-fitted curvilinear grids for the model represent the complete boundary of the area considered by four curves defined by four functions, and the four boundaries of two of the larger islands are then represented approximately by two general functions. An appropriate independent coordinate transformation maps the curvilinear physical area to a square domain, and each island boundary is transformed to a rectangle within this square domain. The vertically integrated shallow water equations are transformed to the new space domain, and solved by a regular explicit finite difference scheme. The model is applied to compute the water levels due to astronomical tides, and also the water levels due to surges associated with tropical storms that hit the coast of Bangladesh.

  • Keywords

Tropical storms surge tide generation shallow water equations boundary-fitted grids Bay of Bengal

  • AMS Subject Headings

35F30 37M05 65N06 65N22 65N50

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COPYRIGHT: © Global Science Press

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@Article{EAJAM-3-27, author = {Farzana Hussain}, title = {A Transformed Coordinates Shallow Water Model for the Head of the Bay of Bengal Using Boundary-Fitted Curvilinear Grids}, journal = {East Asian Journal on Applied Mathematics}, year = {2018}, volume = {3}, number = {1}, pages = {27--47}, abstract = {

The Bay of Bengal is surrounded by coastline except to the south, where there is open sea. The coastline bends most sharply along the coast of Bangladesh, and there are many small and large islands in the offshore region there. In order to incorporate the island boundaries and the curved coastline properly, in any numerical scheme it is often necessary to consider a very fine grid resolution along the coastal belts whereas this is unnecessary away from the coasts. However, a very fine resolution involves more memory and more CPU time in the numerical solution process, and invites numerical instability. On the other hand, boundary-fitted curvilinear grids in hydrodynamic models for coastal seas, bays and estuaries not only fit to the coastline but also render the finite difference schemes simpler and more accurate. In this article, the boundary-fitted curvilinear grids for the model represent the complete boundary of the area considered by four curves defined by four functions, and the four boundaries of two of the larger islands are then represented approximately by two general functions. An appropriate independent coordinate transformation maps the curvilinear physical area to a square domain, and each island boundary is transformed to a rectangle within this square domain. The vertically integrated shallow water equations are transformed to the new space domain, and solved by a regular explicit finite difference scheme. The model is applied to compute the water levels due to astronomical tides, and also the water levels due to surges associated with tropical storms that hit the coast of Bangladesh.

}, issn = {2079-7370}, doi = {https://doi.org/10.4208/eajam.130612.210213a}, url = {http://global-sci.org/intro/article_detail/eajam/10842.html} }
TY - JOUR T1 - A Transformed Coordinates Shallow Water Model for the Head of the Bay of Bengal Using Boundary-Fitted Curvilinear Grids AU - Farzana Hussain JO - East Asian Journal on Applied Mathematics VL - 1 SP - 27 EP - 47 PY - 2018 DA - 2018/02 SN - 3 DO - http://doi.org/10.4208/eajam.130612.210213a UR - https://global-sci.org/intro/article_detail/eajam/10842.html KW - Tropical storms KW - surge KW - tide generation KW - shallow water equations KW - boundary-fitted grids KW - Bay of Bengal AB -

The Bay of Bengal is surrounded by coastline except to the south, where there is open sea. The coastline bends most sharply along the coast of Bangladesh, and there are many small and large islands in the offshore region there. In order to incorporate the island boundaries and the curved coastline properly, in any numerical scheme it is often necessary to consider a very fine grid resolution along the coastal belts whereas this is unnecessary away from the coasts. However, a very fine resolution involves more memory and more CPU time in the numerical solution process, and invites numerical instability. On the other hand, boundary-fitted curvilinear grids in hydrodynamic models for coastal seas, bays and estuaries not only fit to the coastline but also render the finite difference schemes simpler and more accurate. In this article, the boundary-fitted curvilinear grids for the model represent the complete boundary of the area considered by four curves defined by four functions, and the four boundaries of two of the larger islands are then represented approximately by two general functions. An appropriate independent coordinate transformation maps the curvilinear physical area to a square domain, and each island boundary is transformed to a rectangle within this square domain. The vertically integrated shallow water equations are transformed to the new space domain, and solved by a regular explicit finite difference scheme. The model is applied to compute the water levels due to astronomical tides, and also the water levels due to surges associated with tropical storms that hit the coast of Bangladesh.

Farzana Hussain. (1970). A Transformed Coordinates Shallow Water Model for the Head of the Bay of Bengal Using Boundary-Fitted Curvilinear Grids. East Asian Journal on Applied Mathematics. 3 (1). 27-47. doi:10.4208/eajam.130612.210213a
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