A high-order Godunov method for one-dimensional convection-diffusion-reaction problems

In this article we develop a high-order Godunov method for one-dimensional convection-diffusion-reaction problems where convection dominates diffusion . The heart of this method comes from incorporating the diffusion term via the slope of the linear representation (recovery) of the solution on each g rid cell. The method is conservative and explicit. Therefore, it is efficie nt in computing time. For constant coefficient linear convection, diffusion , and Lipschitz-type reaction, the properties of the total variation stabil ity and monotonicity preservation are proved. An error estimation is derive d. Computational examples are presented and compared with the exact solutio ns. (C) 2000 John Wiley & Sons, Inc.