An Eulerian Approach for Vortex Motion Using a Level Set Regularization Procedure
✍ Scribed by Eduard Harabetian; Stanley Osher; Chi-Wang Shu
- Publisher
- Elsevier Science
- Year
- 1996
- Tongue
- English
- Weight
- 422 KB
- Volume
- 127
- Category
- Article
- ISSN
- 0021-9991
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✦ Synopsis
where (x, y, z, t) is the vorticity vector and v(x, y, z, t) is the velocity vector.
We present an Eulerian, fixed grid, approach to solve the motion of an incompressible fluid, in two and three dimensions, in which
In a vortex sheet, is a singular measure concentrated the vorticity is concentrated on a lower dimensional set. Our apon a two-dimensional surface, while in a vortex filament, proach uses a decomposition of the vorticity of the form ϭ P(), is a function concentrated on a tubular neighborhood of in which both (the level set function) and (the vorticity strength a curve.
vector) are smooth. We derive coupled equations for and which
Traditionally, these problems have been solved within give a regularization of the problem. The regularization is topological and is automatically accomplished through the use of numerical a Lagrangian framework, in which the vorticity is carried schemes whose viscosity shrinks to zero with grid size. There is no along by fluid particles [6-9, 2, 17]. Numerical methods need for explicit filtering, even when singularities appear in the based on this approach have the advantage that they adapt front. The method also has the advantage of automatically allowing very well to the flow. On the other hand, they are not topological changes such as merging of surfaces. Numerical examples, including two and three dimensional vortex sheets, two-di-simple to implement in three dimensions and they may mensional vortex dipole sheets, and point vortices, are given. To have difficulties with topological changes, such as merging our knowledge, this is the first three-dimensional vortex sheet calcuof interfaces. Merging may occur for some of these problation in which the sheet evolution feeds back to the calculation of lems (and certainly not for others such as the vortex patch the fluid velocity. Vortex in cell calculations for three-dimensional problem). In addition, some kind of numerical filtering is vortex sheets were done earlier by Trygvasson et al. ᮊ 1996 Academic Press, Inc.