Internal boundary conditions for flood simulation with 2D Shallow water Equations using Finite Volume models: bridge piers

River floodings may strike on urban areas, and practitioners are interested in the simulation of these events. Credible flooding representation requires that obstacles and structures, whose presence can influence the flow characteristics, are taken into account. This is evident for bridge piers, whose presence through the river cross-section may cause the flow level to rise and the overflow above the banks. The 2D Shallow water Equations, which are the preferred mathematical model for flood simulation of large areas, are usually solved employing the Finite Volume Method. In this class of schemes, the obstacles may be included as holes in the computational mesh with reflective boundary conditions representing the corresponding solid walls. Under this conceptual framework, the bridges are taken into account by representing the piers with an adequate mesh discretization where refinements are required to capture the pier geometry (Ratia et al., 2014). However, this procedure leads to increased computational time, as mesh refinement requires both smaller time steps and a higher number of computational cells. Alternative to the approach above, structures and obstacles can be represented in 2D Finite Volume schemes as appropriate internal boundary conditions (Zhao et al., 1994, Morales-Hernández et al., 2013, Ratia et al., 2014, Echevarribar et al., 2019, Cui et al., 2019). Under this framework, structures such as bridges can be represented using a line, corresponding to the bridge axis, through which an appropriate internal boundary condition is applied. In the literature, it has been proposed that internal boundary conditions introduced by structures and obstacles are treated as geometric discontinuities where an appropriate Rieman problem is solved exactly or approximately (Guerra et al., 2011, Han & Warnecke, 2014, Ratia et al. 2014, Cozzolino et al., 2014a, 2015, Echevarribar et al., 2019). Pepe et al. (2019) have used the Riemann problem concept to introduce constrictions and obstructions in the 1D Shallow water Equations model. The effect of a bridge on the flow can be interpreted as an obstruction with multiple opens along the bridge axis. This suggests extending the 1D formulation by Pepe et al. (2019) to the 2D case by taking into account the transverse velocity. In the present work, this approach is presented showing promising results. At some distance from the bridge, the mesh-hole method and the Riemann approach supply similar results, but the Riemann approach allows the use of a coarser mesh and larger computational steps leading to a reduced computational burden.