A well-balanced shallow water flow model on quadtree cut cell grids is presented. The Cartesian cut cell method is applied due to its flexibility in treating curvilinear boundaries. In order to preserve a lake-at-rest and the positivity of water depths in drying/wetting zones, the hydrostatic reconstruction proposed by Audusse et al. [1] is implemented on cut cell grids. In addition, the gradient construction method on cut cells proposed by Causon et al. [8] is modified due to the spurious calculation when a solid boundary is nearly parallel to grids. The numerical schemes mentioned above are employed in Gerris which is open source free software and provides a shallow water solver on adaptive quadtree grids. The applied numerical schemes are validated using four test simulations: still water in an inclined domain; oscillation in a parabolic container; shock reflection by a circular cylinder; flash flood experiment in a model city. The simulation results are compared with analytical solutions, experiment data and the results simulated by other researchers.
A well-balanced shallow water flow model on quadtree cut cell grids is presented. The Cartesian cut cell method is applied due to its flexibility in treating curvilinear boundaries. In order to preserve a lake-at-rest and the positivity of water depths in drying/wetting zones, the hydrostatic reconstruction proposed by Audusse et al. [1] is implemented on cut cell grids. In addition, the gradient construction method on cut cells proposed by Causon et al. [8] is modified due to the spurious calculation when a solid boundary is nearly parallel to grids. The numerical schemes mentioned above are employed in Gerris which is open source free software and provides a shallow water solver on adaptive quadtree grids. The applied numerical schemes are validated using four test simulations: still water in an inclined domain; oscillation in a parabolic container; shock reflection by a circular cylinder; flash flood experiment in a model city. The simulation results are compared with analytical solutions, experiment data and the results simulated by other researchers.