Abstract
We present a well-balanced high-resolution non-oscillatory central finite volume scheme for solving the
shallow water equations with a non-flat bottom topology. Time integration is obtained following a
RungeKutta procedure, coupled with its natural continuous extension. We use a central scheme with
a point value reconstruction algorithm based on average or flux values, which satisfies the monotonicity
preserving property. We apply a special treatment for the source term spatial integration, which preserves
the time and space accuracy and it results in a well-balanced scheme. Several one-dimensional
test cases are used to verify the behaviour and non-oscillatory properties of our scheme.