A finite element BFGS algorithm for the reconstruction of the flow field generated by vortex rings
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Y. Zhang
Abstract
- Vortex rings are generated in numerous practical applications (biological propulsion, internal combustion engines) by the sudden injection of a fluid. Measurements of such flows often provide partial information, generally limited to the exterior of the vortex ring. We propose in this paper a new algorithm for the reconstruction of the stream function inside a bounded domain, where a vortex ring is supposed to form.We derive a quasi-Newton Broyden- Fletcher-Goldfarb-Shanno (BFGS) algorithm for this problem, using a cost function that describes the matching between the reconstructed field and given values of normal derivatives on the boundary of the domain. The algorithm computes the best parameters of the vortex model that is used to describe the vorticity distribution inside the vortex ring. Several vortex models are considered. The method is implemented in freefem++ using a P1 finite-element spatial discretization. Validation tests using analytical models (Hill’s spherical vortex) and Navier-Stokes direct numerical simulation data show good agreement between reconstructed and reference fields.
© 2013 by Walter de Gruyter GmbH & Co.
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- Preface
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- New development in freefem++
- Fictitious domain method to model a movable rigid body in a sound wave
- High performance domain decomposition methods on massively parallel architectures with freefem++
- Solution of 2D Boussinesq systems with freefem++: the flat bottom case
- A finite element BFGS algorithm for the reconstruction of the flow field generated by vortex rings
- Author Index
Articles in the same Issue
- Masthead
- Preface
- A non-standard FETI-DP mortar method for Stokes problem
- Implementation of a low order mimetic elements in freefem++
- Moving meshes with freefem++
- Mathematical modeling of heat treatment for a steering rack including mechanical effects
- A scenario for symmetry breaking in Caffarelli–Kohn–Nirenberg inequalities
- New development in freefem++
- Fictitious domain method to model a movable rigid body in a sound wave
- High performance domain decomposition methods on massively parallel architectures with freefem++
- Solution of 2D Boussinesq systems with freefem++: the flat bottom case
- A finite element BFGS algorithm for the reconstruction of the flow field generated by vortex rings
- Author Index
