Discontinuous Galerkin finite element approximation of the two-dimensional Navier-Stokes equations in stream-function formulation
In this paper, we present the construction and computational assessment of an hp-version discontinuous Galerkin finite element method (DGFEM) for the numerical solution of the Navier-Stokes equations governing 2D stationary incompressible flows. Using a stream-function formulation, which ensures tha...
| Príomhchruthaitheoirí: | , , |
|---|---|
| Formáid: | Conference item |
| Foilsithe / Cruthaithe: |
2007
|
| _version_ | 1826288598216867840 |
|---|---|
| author | Mozolevski, I Sueli, E Boesing, P |
| author_facet | Mozolevski, I Sueli, E Boesing, P |
| author_sort | Mozolevski, I |
| collection | OXFORD |
| description | In this paper, we present the construction and computational assessment of an hp-version discontinuous Galerkin finite element method (DGFEM) for the numerical solution of the Navier-Stokes equations governing 2D stationary incompressible flows. Using a stream-function formulation, which ensures that the incompressibility constraint is automatically satisfied, we reduce the system of Navier-Stokes equations to a single fourth-order nonlinear partial differential equation. We introduce a discretization of this fourth-order nonlinear partial differential equation based on a combination of the symmetric DGFEM for the biharmonic part of the equation and a DGFEM with jump-penalty terms for the hyperbolic part of the problem, and then we solve the resulting nonlinear problem using Newton's method. Numerical examples, including the solution of the 2D lid-driven cavity flow problem, are presented to demonstrate the convergence and accuracy of the method. Copyright © 2006 John Wiley and Sons, Ltd. |
| first_indexed | 2024-03-07T02:16:07Z |
| format | Conference item |
| id | oxford-uuid:a24b1b99-9c6f-473a-b3a1-4cb4a01c3e91 |
| institution | University of Oxford |
| last_indexed | 2024-03-07T02:16:07Z |
| publishDate | 2007 |
| record_format | dspace |
| spelling | oxford-uuid:a24b1b99-9c6f-473a-b3a1-4cb4a01c3e912022-03-27T02:19:11ZDiscontinuous Galerkin finite element approximation of the two-dimensional Navier-Stokes equations in stream-function formulationConference itemhttp://purl.org/coar/resource_type/c_5794uuid:a24b1b99-9c6f-473a-b3a1-4cb4a01c3e91Symplectic Elements at Oxford2007Mozolevski, ISueli, EBoesing, PIn this paper, we present the construction and computational assessment of an hp-version discontinuous Galerkin finite element method (DGFEM) for the numerical solution of the Navier-Stokes equations governing 2D stationary incompressible flows. Using a stream-function formulation, which ensures that the incompressibility constraint is automatically satisfied, we reduce the system of Navier-Stokes equations to a single fourth-order nonlinear partial differential equation. We introduce a discretization of this fourth-order nonlinear partial differential equation based on a combination of the symmetric DGFEM for the biharmonic part of the equation and a DGFEM with jump-penalty terms for the hyperbolic part of the problem, and then we solve the resulting nonlinear problem using Newton's method. Numerical examples, including the solution of the 2D lid-driven cavity flow problem, are presented to demonstrate the convergence and accuracy of the method. Copyright © 2006 John Wiley and Sons, Ltd. |
| spellingShingle | Mozolevski, I Sueli, E Boesing, P Discontinuous Galerkin finite element approximation of the two-dimensional Navier-Stokes equations in stream-function formulation |
| title | Discontinuous Galerkin finite element approximation of the two-dimensional Navier-Stokes equations in stream-function formulation |
| title_full | Discontinuous Galerkin finite element approximation of the two-dimensional Navier-Stokes equations in stream-function formulation |
| title_fullStr | Discontinuous Galerkin finite element approximation of the two-dimensional Navier-Stokes equations in stream-function formulation |
| title_full_unstemmed | Discontinuous Galerkin finite element approximation of the two-dimensional Navier-Stokes equations in stream-function formulation |
| title_short | Discontinuous Galerkin finite element approximation of the two-dimensional Navier-Stokes equations in stream-function formulation |
| title_sort | discontinuous galerkin finite element approximation of the two dimensional navier stokes equations in stream function formulation |
| work_keys_str_mv | AT mozolevskii discontinuousgalerkinfiniteelementapproximationofthetwodimensionalnavierstokesequationsinstreamfunctionformulation AT suelie discontinuousgalerkinfiniteelementapproximationofthetwodimensionalnavierstokesequationsinstreamfunctionformulation AT boesingp discontinuousgalerkinfiniteelementapproximationofthetwodimensionalnavierstokesequationsinstreamfunctionformulation |