To represent a ballistic trajectory with B-spline,Monte Carlo method is used in the simulation of B-spline separating signals method.A suggestion is given on how to add external knots to the internal knots sequence.Consistency of B-spline approximation space is discussed to demonstrate the relevant theorem.Further more,B-spline separating signals method is validated by a comparison with Monte Carlo simulation.It decides efficiently exact knots sequence needed to represent a ballistic trajectory.With the knots sequence,the parameters to be estimated is greatly eliminated.

Gaseous detonation propagation through a bifurcated tube was numerically investigated. A 2^nd additive semi-implicit Runge-Kutta method and a 5^th order WENO scheme were used to solve two-dimensional reactive Euler equations. A detailed chemical reaction model was utilized to describe the heat release of detonation. The contours of density, pressure, temperature, species OH mass fraction, the computed cellular pattern and the traveling speed of detonation were obtained. The results show that, influenced by the rarefaction waves from the left sharp comer, the reaction zone is separated from the leading shock. Then, the detonation is degenerated into the deflagration. The winkled reaction front can be clearly identified in numerical schlieren and temperature contours. Re-initiation is induced by the leading shock reflection on the right wall in the vertical branch. Mach reflection of disturbed detonation occurs in both vertical and horizontal branches. The boundary between regions of uniform and larger cells is not a straight line; it doesn't exactly start at the left sharp comer and is usually upstream of the left sharp comer. The triple-point trajectory characterizing Mach reflection locates downstream of the right comer in the horizontal branch. Complex structures of vortices, the unreacted region, and shock-vortex interaction are observed in flow field around the left comer. Vortices accelerate reaction rates of the unreacted region. The reflected shock interacts with vortices and breaks them into pieces. Reflected shock also accelerates the consumption of the unreacted region and then an embedded jet is produced. The evolution of detonation wave and computed cellular pattern are qualitatively consistent with those from experiments.