Investigating the impact of spatial and temporal coefficients on numerical solution of kinematic wave using Preissmann scheme

The finite difference solution of kinematic waves using Pressmann scheme is the main issue of this research. The Pressmann scheme depends on several weighting coefficients which appear in the discretization of temporal and spatial partial derivatives. The objective of the curent study is to investigate the sensitivity of the solution to these weighting coefficients and to introduce some limitations on the coefficients in terms of numerical stability. A numerical model using Pressmann scheme is developed and verified for solution of kinematic wave equations. The sensitivity analysis is carried out to explore the impact of weighting coefficients on the results. The results of the research show that the Preissmann finite difference soulution of kinematic waves is significantly sensitive to the weighting coefficients. The solution becomes unstable for some values of the spatial and temporal coefficients. Moreover, as the temporal and/or spatial coefficients increase, the degree of attenuation increases as well. Based on the von Neumann stability analysis, a relationship which constrains the weighting coefficients for the stabiligy is presented at the end.

Keywords:

Kinematic wave , Pressmann scheme , Wighting coefficients