Balance errors generated by numerical diffusion in the solution of non-linear open channel flow equations

Dariusz Gąsiorowski

doi:10.1016/j.jhydrol.2012.11.008

Balance errors generated by numerical diffusion in the solution of non-linear open channel flow equations

Abstract

The paper concerns the untypical aspect of application of the dissipative numerical methods to solve nonlinear hyperbolic partial differential equations used in open channel hydraulics. It is shown that in some cases the numerical diffusion generated by the applied method of solution produces not only inaccurate solution but as well as a balance error. This error may occur even for an equation written in the conservative form not only in the solution containing a shock wave but also for the smooth solution with strong gradients. In order to explain this problem 1-D kinematic wave equation and 1-D system of shallow water equations, both solved by the finite-difference implicit box scheme, are considered. Accuracy analysis carried out using the modified equation approach revealed why the numerical solutions of these equations written in the conservative forms contain the balance errors. It was shown that the balance error is directly connected with the additional source term generated by the numerical diffusion during the solution of equation written in an inadequate conservative form. Consequently the balance error depends on the values of time step, spatial interval and the weighting parameters involved in the applied method of solution.

Citations

8

CrossRef
0

Web of Science
9

Scopus

Author (1)

Dariusz Gąsiorowski dr hab. inż.

Cite as

Full text

full text is not available in portal

full content of the article see on external site open in new tab

Keywords

Details

Category:: Articles
Type:: artykuł w czasopiśmie wyróżnionym w JCR
Published in:: JOURNAL OF HYDROLOGY no. 476, pages 384 - 394,
ISSN: 0022-1694
Language:: English
Publication year:: 2013
Bibliographic description:: Gąsiorowski D.: Balance errors generated by numerical diffusion in the solution of non-linear open channel flow equations// JOURNAL OF HYDROLOGY. -Vol. 476, (2013), s.384-394
DOI:: Digital Object Identifier (open in new tab) 10.1016/j.jhydrol.2012.11.008
Verified by:: Gdańsk University of Technology