Surface flow formula (Water Overlay)
Imbalances in water levels across the grid drive the flow of water until a state of equilibrium is reached in terms of h (the height of the water column) and flux. Behavior of the flow is described by a second-order semi-discrete central-upwind scheme produced by Kurganov and Petrova (2007)[1], which is based on the 2-D Saint-Venant equations (a.k.a. shallow water equations):
- Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \begin{align} \frac{\partial h}{\partial t} &+ \frac{\partial (hu)}{\partial x} + \frac{\partial (hv)}{\partial y} = 0,\\[3pt] \frac{\partial (hu)}{\partial t} &+ \frac{\partial}{\partial x} \left( hu^2 + \frac{1}{2} gh^2 \right) + \frac{\partial (huv)}{\partial y} = -gh \frac{\partial B}{\partial x} - ghn^2u \sqrt{u^2 + v^2} h^{-\frac{4}{3}},\\[3pt] \frac{\partial (hv)}{\partial t} &+ \frac{\partial (huv)}{\partial x} + \frac{\partial}{\partial y} \left( hv^2 + \frac{1}{2} gh^2 \right) = -gh \frac{\partial B}{\partial y} - ghn^2u \sqrt{u^2 + v^2} h^{-\frac{4}{3}}, \end{align} }
where
u is the velocity in the x-direction v is the velocity in the y-direction h is the water depth B is the bottom elevation g is the acceleration due to gravity n is the Gauckler–Manning coefficient
See also
References
- ↑ Kurganov A, Petrova G (2007) ∙ A Second-Order Well-Balanced Positivity Preserving Central-Upwind Scheme for the Saint-Venant System ∙ found at: http://www.math.tamu.edu/~gpetrova/KPSV.pdf (last visited 2019-04-11)