Numerical solution of dispersion equation in one dimension

Abstract

An improved hybrid method for one‐dimensional advection‐diffusion problems, based on the Holly‐Preissmann two‐point fourth‐order and Crank‐Nicholson numerical schemes, has been proposed to handle the problem with Courant numbers (Cr) greater than 1. Extensive test runs and analyses have been performed for a schematic advection‐diffusion problem. Through a comparison of the analytical solution with the computed results, the accuracy and stability of this improved hybrid method are discussed. Satisfactory results are found for both weak and strong diffusion problems under large Courant number conditions. The sensitivity of the improved method to the temporal weighting factor has also been demonstrated. For strong diffusion problems, the use of a larger temporal weighting factor becomes necessary to eliminate the phenomenon of instability.