The prediction of critical points for thermal explosions in a finite volume

A technique for predicting critical points for thermal ignition by solving specific extended systems of equations is presented. In particular, two extended systems for locating limit points and nondegenerate hysteresis points are discussed. These are implemented in a finite-element formulation, which allows the points of ignition, extinction, and loss of criticality to be calculated for explosions in a finite volume of arbitrary shape. This is demonstrated for the special case of thermal ignition in a finite cylinder. Continuation methods are used to follow the paths of critical points as the aspect ratio of the cylinder varies.