.. .. Development,

, 187 6.2.1 Basic design of nested model

.. .. Grid-comparison,

, Case 1: Multiple nested grids for linear 2DSWEs for structured grids, p.189

, Case 2: Multiple nested grids for 2DNSWEs for structured grids, p.192

, Comparison of one-way and two-way nesting by using different schemes, p.199

, Comparison between one-way and two-way nesting When the time step in a coarse grid is the same time step in a fine grid and the space refinement ratio is 1:3, vol.202

, Case 1: For 2D depth-averaged linear shallow water equation, p.202

, Case 2: For 2D depth-averaged nonlinear shallow water equation, p.203

, The space refinement ratio is 1:3 and temporal refinement ratio is 1:2 when ? ? = ? 204 temporal refinement ratio are 1:3

, Multiply nested techniques for 2DSWEs when the type of structured grids (adjacent/separate)

C. .. Summary,

, 2.1 Example 1: When the space refinement ratio is 1:5 and the temporal refinement ratio is 1:2 for 2DNSWEs, Contents 7.1 Two-Way nesting grid Algorithm

, Example 3: When the space refinement ratio is 1:5 and temporal refinement ratio is 1:2 for linear 2DSWEs, 2 Example 2: Comparison the numerical solutions of the nested grid at multiple levels when the space refinement ratio is 1:3 and 1:5 and temporal refinement ratio is 1

. .. , Comparison 2-between the free surface, u-velocity and v-velocity when the space refinement is 1:5 and temporal refinement is 1:2, Example, vol.8, p.226

C. .. Summary,

=. =150, ?. =?-=1, and ?. =0, 00015s in a fine grid when the space refinement is 1:5 and temporal refinement is 1:2 with CFL condition 0.02. The following figure shows 2-of free surface elevation

.. .. Development,

.. .. Numerical-results,

, Case 1: When the space refinement ratio is 1:5 and temporal refinement ratio is 1:2 for 2D nonlinear SWEs

, 242 8.4.1 Comparison 2-for the free surface in cases separate grids and embedded grids, When the space refinement ratio is 1:5 and temporal refinement ratio is 1:2 for linear 2DSWEs, vol.2

. .. For-linear-swes,

, 249 8.5.1 Example 1 : Case 1 : Coupling (embedding) systems for 2D nonlinear SWEs 249 8.5.2 Example 2: Case 2: Coupling systems for 2D non-linear shallow water equations, Coupling three systems when the space refinement ratio 1:5 with no refinement of time, vol.3

, Case 3: Coupling systems for 2D nonlinear / linear shallow water equations, vol.3, p.251

C. .. Summary,

, For all examples, we use the formulas of numerical discretization 2DSWEs given in Sections 2.4, 2.5, and 2.6 and we find 2-of free surface elevation in two-way nested grids

, The bottom friction comes from Manning's formula which is uniform throughout the grids, where n is roughness coefficient

, All simulations are made using moving boundary conditions, we use a nested grid with interface Recommendations (Future Works)

, Apply two-way interaction for multiple nested grids in some applications of life such that weather and climate models in Coordinates spherical using an explicit finite difference methods or finite volume methods

, Apply a two-way nesting technique using an explicit finite difference method and leapfrog with Robert-Asselin filter with radative open boundary condition

, Apply a new technique of two-way nesting grids in some application life for example hydrodynamic model for the port of new york for 3DSWEs with moving boundary condition

, Study an existence of solutions for shallow water models with non-homogenous boundary conditions, global weak solution and smoothness

, Apply two-way interaction technique for multiple nested grids of 2DSWEs when a specific domain rotation is required using the explicit methods

, Apply two-way interaction technique for SWEs using irregular geometry boundary conditions

, Study two-way nesting grid for ocean models when the water depth discontinuous with moving boundary conditions

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