Abstract
AbstractThe discretization of partial differential equations can produce numerical errors, and in particular symmetry errors. Typically the symmetry is fitted into the numerical method based on the relative merits of physically aligning the mesh, solving in the natural coordinate frame or modifying the truncation error. In this paper we will consider two alternative approaches developed from capturing the underlying symmetries, inherent in the partial differential equations, in the numerical method. The invariant numerical methods are developed from the extension of Lie group theory to discretized equations using discrete invariants and the technique of invariantization for the heat equation. Their performances against more traditional schemes will be presented. © British Crown Copyright 2008/MOD. Reproduced with permission. Published by John Wiley & Sons, Ltd.
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 callMore From: International Journal for Numerical Methods in Fluids
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.
