  This paper reports high resolution simulations using a fifth-order weighted
essentially non-oscillatory (WENO) scheme with a third order TVD Runge-Kutta
time stepping method to examine the features of detonation front and physics in
square ducts. The simulations suggest that two and three-dimensional detonation
wave front formations are greatly enhanced by the presence of transverse waves.
The motion of transverse waves generates triple points (zones of high pressure
and large velocity coupled together), which cause the detonation front to
become locally overdriven and thus form "hot spots". The transversal motion of
these hot spots maintains the detonation to continuously occur along the whole
front in two and three-dimensions. The present simulations indicate that the
influence of the transverse waves on detonation is more profound in three
dimensions and the pattern of quasi-steady detonation fronts also depends on
the duct size. For a narrow duct (4LX4L where L is the half reaction length),
the detonation front displays a distinctive "spinning" motion about the axial
direction with a well-defined period. For a wider duct (20LX20L), the
detonation front exhibits a "rectangular mode" periodically, with the front
displaying "convex" and "concave" shapes one following the other and the
transverse waves on the four walls being partly out-of-phase with each other.
