Stability analysis of a Galerkin/Runge-Kutta Navier-Stokes discretisation on unstructured tetrahedral grids
This paper presents a timestep stability analysis for a class of discretisations applied to the linearised form of the Navier-Stokes equations on a 3D domain with periodic boundary conditions. Using a suitable definition of the "perturbation energy" it is shown that the energy is monotonic...
| Main Author: | |
|---|---|
| Format: | Journal article |
| Language: | English |
| Published: |
1997
|
| _version_ | 1797071387806924800 |
|---|---|
| author | Giles, M |
| author_facet | Giles, M |
| author_sort | Giles, M |
| collection | OXFORD |
| description | This paper presents a timestep stability analysis for a class of discretisations applied to the linearised form of the Navier-Stokes equations on a 3D domain with periodic boundary conditions. Using a suitable definition of the "perturbation energy" it is shown that the energy is monotonically decreasing for both the original p.d.e. and the semi-discrete system of o.d.e.'s arising from a Galerkin discretisation on a tetrahedral grid. Using recent theoretical results concerning algebraic and generalised stability, sufficient stability limits are obtained for both global and local timesteps for fully discrete algorithms using Runge-Kutta time integration. © 1997 Academic Press. |
| first_indexed | 2024-03-06T22:52:30Z |
| format | Journal article |
| id | oxford-uuid:5f445a4a-e0e4-41af-accf-f2adcd2cfd8d |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-06T22:52:30Z |
| publishDate | 1997 |
| record_format | dspace |
| spelling | oxford-uuid:5f445a4a-e0e4-41af-accf-f2adcd2cfd8d2022-03-26T17:45:49ZStability analysis of a Galerkin/Runge-Kutta Navier-Stokes discretisation on unstructured tetrahedral gridsJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:5f445a4a-e0e4-41af-accf-f2adcd2cfd8dEnglishSymplectic Elements at Oxford1997Giles, MThis paper presents a timestep stability analysis for a class of discretisations applied to the linearised form of the Navier-Stokes equations on a 3D domain with periodic boundary conditions. Using a suitable definition of the "perturbation energy" it is shown that the energy is monotonically decreasing for both the original p.d.e. and the semi-discrete system of o.d.e.'s arising from a Galerkin discretisation on a tetrahedral grid. Using recent theoretical results concerning algebraic and generalised stability, sufficient stability limits are obtained for both global and local timesteps for fully discrete algorithms using Runge-Kutta time integration. © 1997 Academic Press. |
| spellingShingle | Giles, M Stability analysis of a Galerkin/Runge-Kutta Navier-Stokes discretisation on unstructured tetrahedral grids |
| title | Stability analysis of a Galerkin/Runge-Kutta Navier-Stokes discretisation on unstructured tetrahedral grids |
| title_full | Stability analysis of a Galerkin/Runge-Kutta Navier-Stokes discretisation on unstructured tetrahedral grids |
| title_fullStr | Stability analysis of a Galerkin/Runge-Kutta Navier-Stokes discretisation on unstructured tetrahedral grids |
| title_full_unstemmed | Stability analysis of a Galerkin/Runge-Kutta Navier-Stokes discretisation on unstructured tetrahedral grids |
| title_short | Stability analysis of a Galerkin/Runge-Kutta Navier-Stokes discretisation on unstructured tetrahedral grids |
| title_sort | stability analysis of a galerkin runge kutta navier stokes discretisation on unstructured tetrahedral grids |
| work_keys_str_mv | AT gilesm stabilityanalysisofagalerkinrungekuttanavierstokesdiscretisationonunstructuredtetrahedralgrids |