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Lagrangian transport through surfaces in compressible flows. (English) Zbl 1394.37117

The authors extend the Lagrangian transport approach, which allows exact integration of flux through a surface, from the volume-preserving case to the general case of compressible flows. The Eulerian transport integral is transformed into a Lagrangian one. Thus the donating region problem proposed by Q. Zhang [SIAM J. Numer. Anal. 51, No. 5, 2822–2850 (2013; Zbl 1282.65113)] is solved. The general theory is presented for two-dimensional flows and an algorithmic overview is given. The consistency of the implementation is demonstrated for an analytical example, i.e., a divergent rotational linear flow transporting a Gaussian fluid density.
Finally, an example for two-dimensional transport in a cross-channel micromixer is presented, comparing Eulerian and Lagrangian transport approaches. The Matlab implementation is available on GitHub, at {https://github.com/dkarrasch/FluxDoRe2D}.

MSC:

37N10 Dynamical systems in fluid mechanics, oceanography and meteorology
76A02 Foundations of fluid mechanics
76F50 Compressibility effects in turbulence
76N10 Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics
76F25 Turbulent transport, mixing
82C70 Transport processes in time-dependent statistical mechanics

Citations:

Zbl 1282.65113

Software:

SADoRe; FluxDoRe2D; iFEM
PDFBibTeX XMLCite
Full Text: DOI arXiv

References:

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