Central WENO schemes for shallow water movable bed equations

In this work a new numerical method is analysed. The scheme is a Central Weighted Essentially Non Oscillatory (CWENO), third order accurate in time and space. Time accuracy is obtained applying a Runge-Kutta scheme, coupled with the Natural Continuous Extension (NCE); space accuracy is obtained using a convex combination of second order polynomials, which interpolate the cell-averaged values of the state variables. Spurious oscillations are automatically avoided. The main goals of the present work are essentially two: a greater computational efficiency with respect to different high resolution methods; a black-box structure of the code, i.e. detailed information about the eigenstructure of the system of conservation laws is not necessary. This property is very important when movable bed occurs, especially when governing equations of the liquid phase and governing equations of the solid phase are coupled: in such cases the eigenstructure may be very complicated and problem dependent. The model is validated over simple test cases having analytical solution, and over simple one dimensional movable bed cases.