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Research and Reports on Mathematics

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Applications of a Nested Model for 2D Shallow Water equations in Tsunami Model

A new technique for a multiple-nested grid of the tsunami model is applied. This model contains linear and nonlinear 2D shallow water equations in each sub-region and consists of a fine grid model nested 5:1 within a coarse grid large area model. Although the size of the grid varies in each sub-region, physical variables in all sub-regions are solved simultaneously. The model allows for any ratio of grid sizes between two adjacent sub-regions in a nonlinear component of 2D shallow water model. This model adopts staggered explicit infinite difference scheme to solve 2D shallow water equations. A nested grid system dynamically coupled up to some region with different grid resolution. A new algorithm is suggested to allow more efficient and flexible for the grid. In a twoway nested grid model, information (velocity components and free surface elevation) from the coarse mesh scheme could enter and affect to the fine mesh scheme in each time step of the solution process and the information feedback from the fine mesh to the coarse one. Fine grids and coarse grid models are used to verify the relationship between temporal and spatial resolution and model accuracy. To verify the nested multi-grid model, several of the numerical examples are introduced to check the efficiency of the nested multi grid model. The results demonstrate the applicability and benefits of nesting.

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