Fully Well-Balanced Methods for Shallow Water Linearized Moment Model with Friction

In this work, we are interested in the numerical study of hyperbolic shallow water moments equations with smooth bottom topographies and friction terms. We propose first- and second-order well-balanced methods that are able to preserve all its stationary solutions. These methods are based on fully well-balanced reconstruction operators. We show some numerical tests to prove their order of accuracy and well-balanced properties.