Efficient implementation of essentially non-oscillatory shock-capturing schemes, II

In this paper we extend our earlier work on the efficient implementation of ENO (essentially non-oscillatory) shock-capturing schemes. We provide a new simplified expression for the ENO construction procedure based again on numerical fluxes rather than cell-averages. We also consider two improvements which we label ENO-LLF (local Lax-Friedrichs) and ENO-Roe, which yield sharper shock transitions, improved overall accuracy, for lower computational cost than previous implementation of the ENO schemes. Two methods of sharpening contact discontinuities—the subcell resolution idea of Harten and the artificial compression idea of Yang, which those authors originally used in the cell average framework—are applied to the current ENO schemes using numerical fluxes and TVD Runge-Kutta time discretizations. The implementation for nonlinear systems and multi-dimensions is given. Finally, many numerical examples, including a compressible shock turbulence interaction flow calculation, are presented.