Analysis of a new Kolgan-type scheme motivated by the shallow water equations

This paper presents the analysis of two different finite volume schemes for hyperbolic conservation laws: the Kolgan high-resolution scheme, and a new Kolgan-type scheme in which the high-order extrapolation of the conservative variables is used just in the upwind contribution of the numerical flux and source terms. Both schemes are compared in terms of the local truncation error, the stability conditions and the C-property. The schemes are applied to different hyperbolic conservation equations, including the one-dimensional scalar transport equation, the Burgers equation and the 2D shallow water equations, in order to compute the observed order of accuracy and to verify the C-property. When applied to the 2D shallow water equations, the new approach avoids spurious oscillations in the solution without the need of using high-order corrections in the definition of the bed slope source term.