NUMERICAL SOLUTION OF SHALLOW WATER EQUATIONS OVER DISCONTINUOUS BED TOPOGRAPHY USING CENTRAL UPWIND METHOD

Date

2023-9-06

Author

Zafer, Sevgi Pınar

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Much effort has been invested in developing numerical methods to solve flow problems over large domains using shallow water models in recent years. Depth integrated shallow water equations can be applied to a variety of problems such as flood inundation. The computation of 2-D overland flow on a horizontal plane is very attractive due to the computational economy achieved by integration over the vertical. However, the bottom boundary may be complicated with sharp discontinuities, especially in urban areas. Numerical methods should produce smooth hydrostatic solutions for the final steady state. This study tests the central upwind scheme in 1-D configurations to reveal its capabilities and limitations. Several properties of the scheme are tested by developing an in-house FORTRAN code named CUS1D. The results obtained indicate good shock resolution without any nonphysical oscillations with high accuracy in both smooth regions and near the shock areas at different flow regimes. The convergence to the steady state solution is verified in flow at rest. Grid dependency, volume conservation, stability and especially maintenance of the equilibrium are discussed for certain generic test cases. The results are validated with other numerical solutions, analytical solutions, and measured data.

Subject Keywords

Shallow Water Equations, Finite Volume Method, Well-balanced Schemes, Central Upwind Scheme, Hyperbolic Partial Differential Equations

URI

https://hdl.handle.net/11511/105258

Collections

Graduate School of Natural and Applied Sciences, Thesis