Riemann Solver for 2D Shallow Water Equations Using Finite Volume Method with HLL Scheme for Boundary Numerical Fluxes

This paper presents a Riemann solver implementation using the Finite Volume Method for solving 2D shallow water equations, employing the HLL scheme to compute boundary numerical fluxes with robust dry-bed handling capabilities. The solver features adaptive flux computation that automatically detects and treats dry bed conditions through depth thresholds in the code logic. Designed for compatibility with both structured and unstructured grids, the implementation requires only basic hydraulic parameters: water depth, flow velocity components, and outward normal vectors. When applied to structured grids, the solver demonstrates exceptional precision in simulating water flow trajectories through optimized matrix operations and vectorized computations. For unstructured grids, it utilizes efficient search algorithms and neighbor connectivity data structures to maintain rapid processing speeds while ensuring numerical stability during flow simulations. The code architecture incorporates modular boundary condition handlers, allowing straightforward implementation and analysis of various boundary types (open, closed, or special conditions) through configurable input parameters. This flexibility enables comprehensive study of flow behavior patterns under different scenarios, with the HLL flux approximation providing reliable shock-capturing capabilities for hydraulic applications.