On an approximate Lax-Wendroff discontinuous Galerkin discretization of hyperbolic system of conservation laws

Abstract: In this talk, we discuss a high-order  discretization of the hyperbolic system of conservation laws. As a high-order method, the Lax–Wendroff time discretization is an alternative method to the popular total variation diminishing Runge–Kutta time discretization of discontinuous Galerkin schemes. The resulting fully discrete schemes are known as LWDG and RKDG methods, respectively. Although LWDG methods are in general more compact and efficient than RKDG methods of comparable order of accuracy, the formulation of LWDG methods involves the successive computation of exact flux derivatives.  The proposed method avoids the computation of exact flux derivatives and is easier to implement than their original LWDG versions. In particular, the formulation of the time discretization of the proposed method does not depend on the flux being used. Numerical results for the scalar and system cases in one and two space dimensions indicate it is more efficient in terms of error reduction per CPU time than LWDG methods of the same order of accuracy. Moreover, increasing the order of accuracy leads to substantial reductions of numerical error and gains in efficiency for solutions that vary smoothly.