This study presents a numerical simulation of detonation waves in insensitive high explosives (IHE). A direct numerical simulation (DNS) method of detonation waves propagation was developed. It solves two-dimensional reactive Euler equations by using a semi-discrete node-centered finite-volume (NCFV) scheme on triangle mesh. Employing ZND model analytical solution as the initial condition, the upper and lower boundary conditions were designed as local sonic equilibrium conditions. The DNS method was validated using steady detonation wave propagation experimental results for tri-amino-tri-nitro-benzene (TATB) based explosives. The two-dimensional steady detonation propagation of the circular arc experiments was completed using a non-embedded technique (electric and optical fibre probe velocimetry). The comparison results demonstrate that the numerical method can provide a good prediction of the pseudo-steady-state detonation wave front propagation and the angular speed.