A high-resolution hydrological solver that solves on time-adaptive grids is created. The solver uses h-refinement strategies which adapts the resolution of the grid using a posteriori measure. It is based on an open-source scientific computing library named PETSc. With the use of highly scalable time-stepping solvers provided by PETSc, an optimised numerical model is obtained. Validation tests are conducted using dam-break scenarios and flow over humps. Strong scaling tests are conducted to test the scalability of the solver. The model is found to be robust and could thus provide accurate flood-forecasting information.