The computational challenge of predicting shock-turbulence interactions stems from the fundamentally different physics at play. Shock waves are microscopically thin regions wherein flow properties change rapidly over a distance roughly equal to the molecular mean free path; hence, they are essentially strong discontinuities in the flow field. Turbulence, on the other hand, is a chaotic phenomenon with broadband spatial and temporal scales of motion. Most shock-capturing methods rely on strong numerical dissipation to artificially smooth the discontinuity, such that it can be resolved on the computational grid. Unfortunately, the artificial dissipation necessary for capturing shocks has a deleterious effect on turbulence. An additional problem is the fact that shock-capturing schemes are typically based on one-dimensional Riemann solutions that are not strictly valid in multiple dimensions. This can lead to anisotropy errors and grid-seeded perturbations. Other complications arising from upwinding, flux limiting, operator splitting etc., can seriously degrade performance and generate significant errors, especially in multiple dimensions. The purpose of this work is to design improved algorithms, capable of capturing both shocks and turbulence, which also scale to tens of thousands of processors. We have evaluated two new hydrodynamic algorithms, in relation to the widely used WENO method, on a suite of test cases. The new methods, referred to as the 'Compact' and 'Hybrid' schemes, show very promising results
