  A kinetic model based on the Particles on Demand method is introduced for gas
phase detonation hydrodynamics in conjunction with the Lee--Tarver reaction
model. The proposed model is realized on two- and three-dimensional lattices
and is validated with a set of benchmarks. Quantitative validation is performed
with the Chapman--Jouguet theory up to a detonation wave speed of Mach 20 in
one dimension. Two-dimensional outward expanding circular detonation is tested
for isotropy of the model as well as for the asymptotic detonation wave speed.
Mach reflection angles are verified in setups consisting of interacting strong
bow shocks emanating from detonation. Spherical detonation is computed to show
viability of the proposed model for three dimensional simulations.
