Wj. Rider, METHODS FOR EXTENDING HIGH-RESOLUTION SCHEMES TO NONLINEAR-SYSTEMS OFHYPERBOLIC CONSERVATION-LAWS, International journal for numerical methods in fluids, 17(10), 1993, pp. 861-885
In extending high-resolution methods from the scalar case to systems o
f equations there are a number of options available. These options inc
lude working with either conservative or primitive variables, characte
ristic decomposition, two-step methods, or component-wise extension. I
n this paper, several of these options are presented and compared in t
erms of economy and solution accuracy. The characteristic extension wi
th either conservative or primitive variables produces excellent resul
ts with all the problems solved. Using primitive variables, the two-st
ep formulation produces high-quality results in a more economical mann
er. This method can also be extended to multiple dimensions without re
sorting to dimensional splitting. Proper selection of limiters is also
important in non-characteristic extension to systems.