| In this thesis, the Space-Time Conservation Element and Solution Element (CE/SE) method has been extended for hyperbolic systems of conservation laws with a stiff, nonlinear source term. Numerical results for detonations were compared with analytical solutions and those obtained by conventional schemes and showed a good agreement with them.; Both steady and unsteady detonations were considered in calculation. In both cases, steady profiles of flow properties based on the ZND theory are used as the initial conditions. A brief outline of the CE/SE method was provided, including space-time integration formulation and discretization schemes. In addition, numerical treatments of stiff source terms based on integration over the conservation element are also illustrated.; The CE/SE scheme was extended to the one and multiple dimensional, unsteady Euler equations for chemically reacting flow. Numerical studies of stable and unstable detonations were conducted for the piston problem and the instability problem. Results are compared with Erpenbeck's solutions for the piston problems and Bourlioux's solutions for the instability problems. Numerical results of detonation initiations in cold reactive gaseous mixtures by a hot reactive pocket were also presented. The initiation, transition, and quenching of the weak detonation are calculated.; The Chapter four deals with the implementation of the CE/SE method to the two-dimensional unsteady reactive Euler equations. A numerical study of two-dimensional detonations was performed to capturing all salient features of complex flow physics of detonations, including cellular structures, triple points, and counter-rotated vortices. When the triple points collide, a new Mach stem is created and a vortex pair detaching from the leading incident shock, and propagating downstream can be observed. Results by the present approach show details of cellular structure perhaps clearer than previously published results. |
