The aim of this work is to find a stable scheme which would solve the Stokes problem of the fluid flow, in which an elastic structure is immersed. Unlike most of the schemes solving fluid-structure interaction problems, in our scheme meshes of fluid and structure do not have to coincide. We have restricted ourselves to two-dimensional domain occupied by fluid with one-dimensional im- mersed structure. To describe a fluid-structure interaction, we have used an Immersed boundary method. At first we consider the strucure to be massless. We have modified an existing scheme and made it unconditionally stable, which was mathematically proven and numerically tested. Then we have proposed a modification where the structure is not massless and also proved the uncondi- tional stability in this case. The proposed schemes were implemented using the Freefem++ software and tested on aneurysm-like geometry. We have tested the behavior of our scheme in case when the qrowing aneurysm touches an obstacle, for example a bone (with no-slip condition on the bone boundary). Powered by TCPDF (www.tcpdf.org)
| Identifer | oai:union.ndltd.org:nusl.cz/oai:invenio.nusl.cz:331228 |
| Date | January 2015 |
| Creators | Zábojníková, Tereza |
| Contributors | Hron, Jaroslav, Feistauer, Miloslav |
| Source Sets | Czech ETDs |
| Language | English |
| Detected Language | English |
| Type | info:eu-repo/semantics/masterThesis |
| Rights | info:eu-repo/semantics/restrictedAccess |
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