JWL++ is a simple Reactive Flow model that includes time-dependent reaction in prompt detonation. It consists of a Murnahan unreacted equation of state, a JWL reacted EOS, a mixer for the two EOS＇s and a single-time-constant exponential rate. The mixing can be done by four ways, using either pressure or pressure plus artificial viscosity in the rate, and also using either an analytic function or a pressure equilibrator. The model reproduces the Size Effect and detonation front curvature. Detonation failure can also be induced. JWL++ propagates also through an arbitrary geometry in 3-D without the need for pre-run program burn calculations. It is slower than a JWL/program "Burn" but faster than "Ignition & Growth".