A finite difference scheme for the incompressible Navier-Stokes equations in 2-dimensionalcurvilinear coordinates is derived. The scheme uses high-order Summation-By-Parts operatorsand boundaries are handled by the Projection method. Using the energy method, the scheme isproven stable and well-posed with Dirichlet boundary conditions for general curvilineartransforms. Numerical tests show convergence of the scheme for high-order operators on theTaylor-Green vortex problem using three different transformations. Furthermore, the Lid-drivencavity problem is tested and it shows that employing curvilinear transforms to create a densergrid near boundaries can achieve greater accuracy when observing boundary layer effects.
| Identifer | oai:union.ndltd.org:UPSALLA1/oai:DiVA.org:uu-478549 |
| Date | January 2022 |
| Creators | Niemelä, David |
| Publisher | Uppsala universitet, Avdelningen för beräkningsvetenskap |
| Source Sets | DiVA Archive at Upsalla University |
| Language | English |
| Detected Language | English |
| Type | Student thesis, info:eu-repo/semantics/bachelorThesis, text |
| Format | application/pdf |
| Rights | info:eu-repo/semantics/openAccess |
| Relation | UPTEC F, 1401-5757 ; 22038 |
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