Finite-difference methods for computing the turning point of ignition in a tubular reactor operated adiabatically Original Research Article

A system of partial differential equations (PDEs) is derived to compute the point of ignition (with respect to the Damköhler number) in an adiabatically-operated tubular reactor in which a first-order, exothermic and irreversible A → B reaction takes place. The temperature-dependent rate constant is assumed to obey the Arrhenius Law. A family of numerical methods using finite-difference approximations is developed to integrate the system of PDEs. The numerical schemes are analysed for stability by a linearized von Neumann method. Two numerical methods are selected to compute solutions: the explicit Euler Method in conjunction with global extrapolation and a novel semi-explicit computation scheme.