Flooding Overlay
2D Saint Venant equations
∂l/∂t+∂du/∂x+∂dv/∂y=q_in ∂u/∂t+u ∂u/∂x+v ∂u/∂y+g ∂l/∂x+g u|u ⃗ |/(C^2 d)=0 ∂v/∂t+u ∂v/∂x+v ∂v/∂y+g ∂l/∂y+g v|u ⃗ |/(C^2 d)=0 Where: d water depth (m + bottom) l water level (m + reference) u velocity in x-direction (m/s) v velocity in y-direction (m/s) qin lateral boundary condition (m/s) t time (s) g gravitation constant (9.80655 m/s2) C Chezy-coefficient (m1/2/s): C= d^(1/6)/n n Manning coefficient (s/m1/3) |u ⃗ | velocity magnitude: √(u^2+v^2 )
Explicit numerical scheme
The Tygron Engine Inundation module relies on an explicit finit volume method, taken from Kurganov and Petrova (2007). This scheme relies on a reconstruction of cell bottom, water level and velocity at the interfaces between computational cells as proposed by Lax and Wendroff (see Rezzolla, 2011). The reconstruction method, taken from Bolderman et all (2014) ensures numerical stability, especially at the wetting and drying front of a flood wave.
Computational time step
References
- Rezzolla L (2011) ∙ Numerical Methods for the Solution of Partial Differential Equations
- Bollermann A, Chen G, Kurganov A and Noelle S (2014) ∙ A Well-Balanced Reconstruction For Wetting/Drying Fronts https://www.researchgate.net/publication/269417532_A_Well-balanced_Reconstruction_for_Wetting_Drying_Fronts
- Kurganov A, Petrova G (2007) ∙ A Second-Order Well-Balanced Positivy Preserving Central-Upwind Scheme for the Saint-Venant System ∙ http://www.math.tamu.edu/~gpetrova/KPSV.pdf