Investigation into the accuracy, stability and parallel performance of a highly stable explicit technique for stiff reaction-transport PDEs

摘要

The numerical simulation of chemically reacting flows is a topic, that has attracted a great deal of current research. At the heart of numerical reactive flow simulations are large sets of coupled, nonlinear Partial Differential Equations (PDES). Due to the stiffness that is usually present, explicit time differencing schemes are not used despite their inherent simplicity and efficiency on parallel and vector machines, since these schemes require prohibitively small numerical stepsizes. Implicit time differencing schemes, although possessing good stability characteristics, introduce a great deal of computational overhead necessary to solve the simultaneous algebraic system at each timestep. This thesis examines an algorithm based on a preconditioned time differencing scheme. The algorithm is explicit and permits a large stable time step. An investigation of the algorithm's accuracy, stability and performance on a parallel architecture is presented.