Open AccessStrong Stability Preserving Runge-Kutta Methods Applied to Water Hammer Problem
Author(s) -
Douglas Frederico Guimarães Santiago,
A. F. Antunis,
D. R. Trindade,
W. J. S. Brandão
Publication year - 2022
Publication title -
trends in computational and applied mathematics
Language(s) - English
Resource type - Journals
ISSN - 2676-0029
DOI - 10.5540/tcam.2022.023.01.00063
Subject(s) - runge–kutta methods , water hammer , stability (learning theory) , mathematics , ordinary differential equation , method of lines , dependency (uml) , l stability , partial differential equation , space (punctuation) , method of characteristics , mathematical analysis , differential equation , computer science , mechanics , differential algebraic equation , physics , software engineering , machine learning , operating system
The characteristic method of lines is the most used numerical method applied to the water hammer problem. It transforms a system of partial differential equations involving the independent variables time and space in two ordinary differential equations along the characteristics curves and then solve it numerically. This approach, although showing great stability and quick execution time, creates ∆x-∆t dependency to properly model the phenomenon. In this article we test a different approach, using the method of lines in the usual form, without the characteristics curves and then applying strong stability preserving Runge-Kutta Methods aiming to get stability with greater ∆t.