A Voronoi finite volume model for riverine and coastal shallow water flows is verified using manufactured bathymetry. In contrast to classical approaches based on artificial forcing, domain geometries are constructed such that prescribed solutions satisfy the governing equations exactly, enabling analytical reference solutions without modification of the equations. This allows verification to remain consistent with physical model formulations commonly used in geophysical applications.
The approach is applied to a fully unstructured Voronoi discretization, demonstrating that verification can be performed on complex meshes without requiring simplified geometries. Numerical results are compared against the constructed analytical solutions, assessing accuracy and sensitivity with respect to mesh irregularity, geometric complexity, and time step variation.
The framework provides a practical route for verification of shallow water models on unstructured meshes, particularly in settings where the introduction of artificial forcing is not admissible.