5 DIFFUSION EQUATION
- Spectral/hp Element Methods for Computational Fluid Dynamics
Spencer J. Sherwin
- Oxford University Press
This chapter considers the diffusion equation: an implicit in time discretization leads to the Helmholtz equation. Both the temporal discretization and eigenspectra of second-order operators that dictate time-step restrictions are discussed. Appropriate preconditioning techniques for inversion of the stiffness matrix, non-smooth solutions due to geometric singularities, and recent advances in three-dimensional domains are discussed. The exercises at the end of the chapter build on the exercises of Chapters 3 and 4 to implement a two-dimensional standard Galerkin hp solution to the Helmholtz problem.
Galerkin discretization, temporal discretization, eigenspectra, non-smooth domains, Helmholtz problem, spectral/hp element solver
Oxford Scholarship Online requires a subscription or purchase to access the full text of books within the service. Public users can however freely search the site and view the abstracts and keywords for each book and chapter.
Please, subscribe or login to access full text content.
If you think you should have access to this title, please contact your librarian.
To troubleshoot, please check our
, and if you can't find the answer there, please