A finite volume scheme for unsteady linear and nonlinear convection-diffusion-reaction problems

Abstract

In the present work, a finite volume scheme (FVS) for simulating spatiotemporal patterns in tubular reactors is proposed without increasing the size of the stencil of the classical finite volume method (FVM) based on central differencing. In discretizing the governing equations of tubular reactors several undetermined weighting parameters are introduced. By letting the truncation error as small as possible the formulas for calculating the weighting parameters is obtained. The proposed FVS is tested by solving the steady-state and time-dependent solutions of convection-diffusion-reaction problems with strong convection and reaction. Results show that the FVS can achieve almost the same accuracy as the exaction solution for the steady-state solutions. When coarse grids are used to solve the time-dependent solutions of convection/reaction dominated convection-diffusion-reaction problems, the FVS not only achieves much higher accuracy, but also shows the incomparable stability advantage compared with the FVM based on the central differencing. Finally, the FVS is employed to study the heat conduction and mass transfer of the tubular reactor. It is found that the feed temperature can be used to control the occurrence of the periodic oscillation of the temperature and mass transfer in the tubular reactor.