A time-splitting numerical technique for solving highly coupled two-phase flow conservation equation

A time-splitting numerical technique incorporating the positive aspects of flux-corrected transport (FCT) and the method of lines (MOL) has been developed to efficiently and accurately solve systems of highly coupled hyperbolic partial differential equations. Several two-phase flow equation systems, including that of modeling deflagration-to-detonation transition (DDT) in granular explosives, are used to illustrate the method. Upwind differencing, MOL, and FCT are also used to solve the model problems so that one can compare the new technique to established methods. The results show that time-splitting offers increased accuracy for these types of problems, although in one dimension the method is computationally more costly. However, in multidimensional calculations, the time-splitting technique should offer an economy of computer cost and storage.