Table of Contents
Journal of Computational Methods in Physics
Volume 2014, Article ID 827034, 13 pages
Research Article

A New Flux Splitting Scheme Based on Toro-Vazquez and HLL Schemes for the Euler Equations

1Department of Physics, Laboratory of Mechanics and Modelling of Physical Systems (L2MPS), Faculty of Science, University of Dschang, P.O. Box 67, Dschang, Cameroon
2Faculté des Sciences et de Technologie, Université des Montagnes, P.O. Box 208, Bangangté, Cameroon
3Laboratory of Industrial and Systems Engineering Environment (LISIE), IUT/FV Bandjoun, University of Dschang, P.O. Box 134, Bandjoun, Cameroon

Received 24 July 2014; Revised 28 October 2014; Accepted 11 November 2014; Published 2 December 2014

Academic Editor: Xavier Ferrieres

Copyright © 2014 Pascalin Tiam Kapen and Tchuen Ghislain. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


This paper presents a new flux splitting scheme for the Euler equations. The proposed scheme termed TV-HLL is obtained by following the Toro-Vazquez splitting (Toro and Vázquez-Cendón, 2012) and using the HLL algorithm with modified wave speeds for the pressure system. Here, the intercell velocity for the advection system is taken as the arithmetic mean. The resulting scheme is more accurate when compared to the Toro-Vazquez schemes and also enjoys the property of recognition of contact discontinuities and shear waves. Accuracy, efficiency, and other essential features of the proposed scheme are evaluated by analyzing shock propagation behaviours for both the steady and unsteady compressible flows. The accuracy of the scheme is shown in 1D test cases designed by Toro.