Abstract
A simple and robust method for solving hyperbolic conservation equations based on the adaptive wavelet-collocation method, which uses a dynamically adaptive grid, are presented. The method utilises natural ability of wavelet analysis to sense localised structures and is based on analysis of wavelet coefficients on the finest level of resolution to create a discontinuity locator function Φ. Using this function, an artificial viscous term is explicitly added in the needed regions using a localised numerical viscosity that ensures the positivity and TVD non-linear stability conditions. Once the wavelet coefficients on the finest level of resolution are below the error threshold parameter ϵ, the artificial viscosity is shut off and any remaining physical waves are free to propagate undamped. Multiple examples in one and two dimensions are presented to demonstrate the method's robustness, simplicity and ease of extending to more complex problems.
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 callMore From: International Journal of Computational Fluid Dynamics
Disclaimer: 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.
