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RESEARCH PRODUCT

A ‘TVD-like’ Scheme for Conservation Laws with Source Terms

R. Donat BeneitoA. Martínez Gavara

subject

Fully developedFlux limitingConservation lawHomogeneousTotal variation diminishingLinear systemScalar (mathematics)Applied mathematicsHigh-resolution schemeMathematics

description

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 on a flux limiting procedure applied only to those terms related to the physical flow derivative.

yearjournalcountryeditionlanguage
2008-09-19
https://doi.org/10.1007/978-3-540-69777-0_31