<p>We present a numerical framework for simulating viscous compressible flows in the presence of solid particles with large size ratios. The volume-filtered Navier-Stokes equations are discretized using a class of high-order low-dissipative finite difference operators with energy-preserving properties. No-slip, adiabatic boundary conditions are enforced at the surface of large particles (with diameters significantly larger than the local grid spacing) using a ghost-point immersed boundary method. Two-way coupling between the gas phase and small particles (with diameters proportional to the grid spacing) is accounted for through volumetric source terms for interphase momentum and energy exchange. A simple and efficient approach for collision detection between small and large particles is proposed. The framework is applied to simulations of planar shocks interacting with bidisperse distributions of particles with size ratios of approximately thirty. Particle dispersion and size segregation are reported and a simple analytical model for size segregation is proposed.</p>