The objective of this work is to derive a shock capturing tool able to treat turbulence with minimum dissipation out of the shock for a large-eddy simulation (LES) of the shock/turbulence interaction. The present numerical modeling of the shock/turbulence interaction consists of a second-order finite volume central scheme using a skew-symmetric form, a Jameson's type artificial dissipation, and the filtered structure function model. We focus on two areas to build simulations of increased accuracy: A new sensor for triggering artificial dissipation is developed to perform LES of the shock/turbulence interaction. This sensor is simple, local, and does not require any a priori knowledge of the shock position. It is first tested in freely decaying turbulence for both viscous and inviscid cases and in the inviscid 2D vortex/shock interaction. It is shown that both shock capturing properties and standard LES results in the case of freely decaying turbulence are recovered. Even though this modified sensor limits dissipation away from the shock, it is shown that the dissipation used inside the shock affects turbulence when eddies cross the shock region. This effect can be minimized by (1) refining the mesh in the vicinity of the shock or (2) pre-filtering. The results obtained by mesh refinement are investigated for the inviscid shock/turbulence interaction in terms of Reynolds stresses and kinetic energy variations accross the shock. A priori testing shows that, with the proposed scheme and for all meshs considered, the dominant dissipation acting on kinetic energy is the SGS dissipation away from the shock and both artificial and SGS dissipation in the shock, the former being larger than the latter.