# Article

**Keywords:**

hyperbolic conservation laws; finite volume method; steady state; semi-implicit central-upwind scheme

**Summary:**

One of the commonly used models for river flow modelling is based on the Saint-Venant equations - the system of hyperbolic equations with spatially varying flux function and a source term. We introduce finite volume methods that solve this type of balance laws efficiently and satisfy some important properties at the same time. The properties like consistency, stability and convergence are necessary for the mathematically correct solution. However, the schemes should be also positive semidefinite and preserve steady states to obtain physically relevant solution of the flow problems. These schemes can also be modified to a high order version or for solving flow problems with a friction source term.