Stability Analysis of Galerkin/Runge-Kutta Navier-Stokes Discretisations on Unstructured 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 monotonically...
| Main Author: | |
|---|---|
| Format: | Report |
| Published: |
Unspecified
1995
|
| _version_ | 1826292383245926400 |
|---|---|
| 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. |
| first_indexed | 2024-03-07T03:13:50Z |
| format | Report |
| id | oxford-uuid:b51da553-4ede-42eb-b9f9-a3acc42f2eaf |
| institution | University of Oxford |
| last_indexed | 2024-03-07T03:13:50Z |
| publishDate | 1995 |
| publisher | Unspecified |
| record_format | dspace |
| spelling | oxford-uuid:b51da553-4ede-42eb-b9f9-a3acc42f2eaf2022-03-27T04:31:02ZStability Analysis of Galerkin/Runge-Kutta Navier-Stokes Discretisations on Unstructured GridsReporthttp://purl.org/coar/resource_type/c_93fcuuid:b51da553-4ede-42eb-b9f9-a3acc42f2eafMathematical Institute - ePrintsUnspecified1995Giles, 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. |
| spellingShingle | Giles, M Stability Analysis of Galerkin/Runge-Kutta Navier-Stokes Discretisations on Unstructured Grids |
| title | Stability Analysis of Galerkin/Runge-Kutta Navier-Stokes Discretisations on Unstructured Grids |
| title_full | Stability Analysis of Galerkin/Runge-Kutta Navier-Stokes Discretisations on Unstructured Grids |
| title_fullStr | Stability Analysis of Galerkin/Runge-Kutta Navier-Stokes Discretisations on Unstructured Grids |
| title_full_unstemmed | Stability Analysis of Galerkin/Runge-Kutta Navier-Stokes Discretisations on Unstructured Grids |
| title_short | Stability Analysis of Galerkin/Runge-Kutta Navier-Stokes Discretisations on Unstructured Grids |
| title_sort | stability analysis of galerkin runge kutta navier stokes discretisations on unstructured grids |
| work_keys_str_mv | AT gilesm stabilityanalysisofgalerkinrungekuttanavierstokesdiscretisationsonunstructuredgrids |