Adaptive Godunov-Based Model for Flood Simulation

Abstract

Godunov-based shallow-water models utilize a discontinuous reconstruction of data at cell faces even for smooth flow, which can cause energy dissipation and degrade accuracy. Analysis of discrete equations shows that jumps (and therefore error) can be minimized by adaptively selecting either primitive or conservative variables for slope limiting and reconstruction according to the local Froude number. Therefore, a Godunov-based model with an adaptive scheme of slope limiting and variable reconstruction is presented. Two practical flood modeling applications are used to compare the performance of the adaptive scheme against two non-adaptive schemes. In addition, performance of second-order accurate schemes is compared to first-order schemes that utilize a second-order accurate description of terrain. Results show that the first-order adaptive scheme possesses the best combination of robustness, efficiency, and accuracy of the tested models.