A method to simulate viscous diffusion of vorticity by convective transport of vortices at a non-solenoidal velocity
A numerical method to simulate viscous diffusion of vorticity using vortex blobs (i.e., without a grid) is presented. The method consists of casting the effects of viscous diffusion into an effective ``diffusion velocity`` at which vortex blobs convect. The diffusion velocity was proposed previously by Ogami and Akamatsu, but they did not consider the effects of the divergence of the diffusion velocity. In fact, the diffusion velocity is highly non-solenoidal, which significantly affects the area over which a vortex blob diffuses. A formulation is presented that relates the area expansion to the diffusion velocity divergence. By taking into account the area expansion, more accurate simulations of diffusion are obtained, as demonstrated by a comparison of numerical and analytical diffusion solutions. Results from simulations show that vortex areas expand significantly in regions of large vorticity gradients. As a result of the area expansion, adjacent vortices remain overlapped, thereby maintaining smooth solution fields. The non-solenoidal diffusion velocity method is easily implemented in vortex blob algorithms, thus facilitating the development of vortex methods to simulate flows with finite Reynolds numbers.
- Research Organization:
- Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
- Sponsoring Organization:
- USDOE, Washington, DC (United States)
- DOE Contract Number:
- AC04-94AL85000
- OSTI ID:
- 10190654
- Report Number(s):
- SAND-93-1763; ON: DE94001777; BR: GB0103012
- Resource Relation:
- Other Information: PBD: Aug 1993
- Country of Publication:
- United States
- Language:
- English
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