High Resolution Shock Capture (HRSC) refers to some Numerical methods of modeling Shock Waves. Generally, they incorporate methods using grids aligned with the flow and shock front.
Shock Waves are not well-modeled by general-purpose fluid dynamics Codes, which generally work well handling values that change only gradually or smoothly over space and time dimensions. Pretty-much by definition, shock means something not like that. Shock Capture Schemes have been developed to handle such special situations. HRSC schemes are recent methods aiming to produce good accuracy efficiently.