This paper describes a method for animating suspended particle explosions. Rather than modeling the numerically troublesome, and largely invisible blast wave, the method uses a relatively stable incompressible fluid model to account for the motion of air and hot gases. The fluid's divergence field is adjusted directly to account for detonations and the generation and expansion of gaseous combustion products. Particles immersed in the fluid track the motion of particulate fuel and soot as they are advected by the fluid. Combustion is modeled using a simple but effective process governed by the particle and fluid systems. The method has enough flexibility to also approximate sprays of burning liquids. This paper includes several demonstrative examples showing air bursts, explosions near obstacles, confined explosions, and burning sprays. Because the method is based on components that allow large time integration steps, it only requires a few seconds of computation per frame for the examples shown.