Flow over a bump

UNDER CONSTRUCTION

Setup

The spatial domain consists of a rectangular

Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle z_b = \begin{cases} 0, & \mbox{if } x < 8 m } \\ 0.2-0.05(x-10)^2, & \mbox{if } 8 \leq x \leq 12 \\ 0, & \mbox{if } x>12 \\ \end{cases} }

(1)

where $\eta$ is the water surface elevation, $\rho$ is the water density, $\rho _{a}$ is the air density, $g$ is the gravitational acceleration, $W$ is the wind speed, $h$ is the water depth, and $C$ is a constant of integration.

Model Setup

A computational grid with constant water depth of 5 m and irregular boundaries is used in order to test the model performance. The computational grid has 60 columns and 70 rows and a constant resolution of 500 m.

Results

Figure 1. Computed water surface elevation for the irregular domain with constant water depth.

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Figure 2. Comparison of computed water surface elevation to the analytical solution for an irregular basin with constant depth.

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Test Cases

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