A new approach for increasing the space and time accuracy of numerical schemes employed in standard (commercial) reservoir simulators is presented in this paper.
We introduce a novel TVD fully second order flux approximation (Two Time Level Flux TTLF) extending the work previously done on applying TVD schemes  to general purpose Black Oil/EOS Compositional reservoir simulators (eg. VIP). The TVD TTLF scheme is a more fundamental application of flux limiters on the second order Taylor's series expansion of the inter-block flux. This enables commercial first order accurate simulators to achieve second order accuracy in both space and time without significantly increasing their complexity.
This paper presents the development of the improved temporal accuracy TVD scheme and the results of the scheme on linear and non-linear 1-D pulse propagation problems and 2-D finely gridded compositional problems.