Search results for "Total variation diminishing"
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Approximate Lax–Wendroff discontinuous Galerkin methods for hyperbolic conservation laws
2017
Abstract The Lax–Wendroff time discretization is an alternative method to the popular total variation diminishing Runge–Kutta time discretization of discontinuous Galerkin schemes for the numerical solution of hyperbolic conservation laws. 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. This procedure allows one to construct schemes of arbitrary formal order of accuracy in space and time. A new approximation procedure avoids the computation of ex…
A ‘TVD-like’ Scheme for Conservation Laws with Source Terms
2008
The theoretical foundations of high-resolution TVD schemes for homogeneous scalar conservation laws and linear systems of conservation laws have been firmly established through the work of Harten [5], Sweby [11], and Roe [9]. These TVD schemes seek to prevent an increase in the total variation of the numerical solution, and are successfully implemented in the form of flux-limiters or slope limiters for scalar conservation laws and systems. However, their application to conservation laws with source terms is still not fully developed. In this work we analyze the properties of a second order, flux-limited version of the Lax-Wendroff scheme preserving steady states [3]. Our technique is based …