The denotation of condensed explosives is very vulnerable to be influenced by the character of its confinement material. Confinements of different materials on the condensed explosives can remarkably change the shock locus and propagation speed of the detonation wave. Especially, when the confinement material has a higher sound-speed than the CJ velocity of explosives, some highly complicated refraction phenomena of detonation waves would take place near the explosives-material interface. This paper aims at analyzing the refraction phenomena of detonation waves in condensed explosives in theoretical and numerical ways. Firstly, an improved shock polar theory based on ZND model of detonation is built to give the styles of the refraction in detonation waves in order to provide a leading-order prediction of the confinement interaction. The improved shock polar is established at the leading shock wave of explosives detonation, and the refraction interaction is determined by the polar curve of the leading shock waves within the unreacted explosives and the polar curve of the refraction shock waves within the confinement material. Secondly, a second-order cell-centered Lagrangian hydrodynamics method, based on the characteristics theory for two-dimensional hyperbolic partial differential equations, is developed to solve the chemically reactive flow equations by the three-term ignition-growth chemistry reaction law. The main character of this method is that the finite volume discretization is adopted and an instantaneous evolution solver from an approximate Galerkin evolution operator is applied to compute the velocity and pressure of a grid vertex in order to update the grid coordinates and evaluate the numerical flux across the cell interface. A representative experiment about the propagation of a slipping detonation wave is numerically simulated. From the theoretical and numerical results about the refraction of detonation waves while the PBX9502 explosives interacting with beryllium interface, there exist four kinds of refraction styles of the detonation wave at high sound-speed material interface: the regular refraction with reflecting shock wave, the irregular refraction with bound precursor wave, the irregular refraction with twin Mach reflection, and the irregular refraction with -wave structure. In the first style, the front of the leading shock wave is straight, the flows in the detonation reactive zone and beryllium are both supersonic, and a reflecting shock wave appears behind the leading shock wave and a refracting shock wave appears within beryllium. In the second style, the front of the leading shock wave is also straight, the flow in the detonation reactive zone is supersonic but the one in beryllium is subsonic, so a reflecting shock wave appears behind the leading shock wave and a refracting shock wave appears within beryllium too; moreover, the refracting shock wave is almost perpendicular to the material interface, that is a bound precursor wave. In the third style, the front of the leading shock wave becomes forward curve, and the flows in the detonation reactive zone and beryllium are both subsonic, i.e., a Mach item is produced at some distance above the material interface where there are two Mach reflection structures on the top and the bottom of the Mach item respectively. Obviously, the bottom Mach reflection is a free precursor wave from the refracting shock wave within beryllium. In the fourth style, the forward curve range of the front of the leading shock wave becomes very broad, and accordingly, the range of subsonic flows in the detonation reactive zone becomes very wide. This makes the top Mach reflection disappear but the bottom one still exist, so the whole structure of the reflection wave seems to be like the Greek alphabet ; meanwhile, the flow within beryllium may be all in a subsonic state.