What numerical schemes are used in computational hydraulics?

Computational hydraulics solves partial differential equations numerically. Schemes: (1) Finite difference - approximate derivatives on structured grid (explicit: simple but stability-limited, implicit: stable but requires matrix solution), (2) Finite volume - conservative, handles discontinuities well (Godunov-type schemes for shock capturing), (3) Finite element - flexible geometry, higher-order accuracy. Time stepping: Crank-Nicolson (2nd order implicit), Preissmann (4-point implicit for rivers). Stability requires CFL condition for explicit schemes. Parallelization and GPU computing enable large-scale 2D/3D simulations. Model selection balances accuracy, computational cost, and application needs.