Abstract
The numerical entropy production (NEP) for shallow water equations (SWE) is discussed and implemented as a smoothness indicator. We consider SWE in three different dimensions, namely, one-dimensional, one-and-a-half-dimensional, and two-dimensional SWE. An existing numerical entropy scheme is reviewed and an alternative scheme is provided. We prove the properties of these two numerical entropy schemes relating to the entropy steady state and consistency with the entropy equality on smooth regions. Simulation results show that both schemes produce NEP with the same behaviour for detecting discontinuities of solutions and perform similarly as smoothness indicators. An implementation of the NEP for an adaptive numerical method is also demonstrated.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
