High order Lax-Wendroff-type schemes for linear wave propagation

The second order accurate Lax-Wendroff scheme is based on the first three terms of a Taylor expansion in time in which the time derivatives are replaced by space derivatives using the governing evolution equations. The space derivatives are then approximated by central difference formulas. In this paper we extent this idea and truncate the...

ADER scheme for the shallow water equations in channel with irregular bottom elevation

In this paper we develop one dimensional non-linear ADER schemes for the shallow water system with source terms. In contrast to conventional schemes we adopt a formulation given in terms of the free surface elevation and water discharge. Data reconstruction is performed using ENO polynomials both for the conservative variables and for the bottom...