METHODS FOR EXTENDING HIGH-RESOLUTION SCHEMES TO NONLINEAR-SYSTEMS OFHYPERBOLIC CONSERVATION-LAWS

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.