High‐resolution methods for preserving the sum of mass fractions: improved χ ‐scheme and an alternative

SUMMARY When high resolution convection schemes are used for discretizing chemical species mass balance equations, the mass fractions are not guaranteed to add to one. We show that a proposed remedy called χ —scheme (Darwish and Moukalled, Comput. Methods Appl. Mech. Engrg. 192 (2003): 1711) will degrade to a diffusive first‐order scheme when a chemical species vanishes from the mixture, for example, because of chemical reactions. We propose an improvement to the χ ‐scheme to overcome this problem. Furthermore, a computationally efficient alternative scheme is proposed and evaluated with several examples, to quantify the improvements in the accuracy and the computational time. Published 2013. This article is a U.S. Government work and is in the public domain in the USA.