An efficient method for the simulation of compressible multimaterial flows with a general form of equation of state is presented for explosive detonation and airblast applications. Multimaterial flows are modeled with a volume-fraction type approach for immiscible fluids governed by the compressible Euler equations on three-dimensional unstructured grids. The five-equation quasi-conservative system is discretized in space using an edge-based finite volume approach with a second-order accurate HLLC approximate Riemann solver and temporal discretization with an explicit multistage Runge–Kutta method. The computational model is robust enough to handle flows with strong shocks, while being general enough to model materials with different equations of state and physical states. Numerical tests demonstrate the accuracy of the method for strong shock and interface interactions. A program burn method is implemented to describe the conversion of solid unreacted explosive to reacted gases in condensed phase detonations. The accuracy of the burn model is validated by comparison with published numerical results of flow profiles during detonation and for near-field airblast. Numerical simulations of hemispherical and plate-shaped explosive charge detonations are performed to investigate the influence of charge shape on airblast. The predicted pressure and impulse from simulation compare well with published experimental data.