On a fluid flow in a thin layer using discontinuous Galerkin method

The contribution deals with a theoretical and experimental investigation of fluid flow in a thin layer when a flow has nearly horizontal nature and negligible vertical acceleration compared with a gravitational one. Under these conditions the full set of Navier-Stokes equations are simplified to the Saint-Venant equations. Several variants of the equations differing by a level of geometry simplification or fluid properties are discussed. A discontinuous Galerkin method was applied for numerical simulations. This method originates from the classical methods of finite volumes but it assumes that inside the elements the searching functions are approximated by the functions of higher orders. Results of numerical simulations are compared with an experimental investigation. The numerical simulations agree very well with the experimental data in the cases when the assumptions made using the derivation of the Saint-Venant equations are fulfilled.