On Donating Regions: Lagrangian Flux through a Fixed Curve

• Autores: Qinghai Zhang
• Localización: SIAM Review, ISSN 0036-1445, Vol. 55, Nº. 3, 2013, págs. 443-461
• Idioma: inglés
• DOI: 10.1137/100796406
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• Resumen

  • Lagrangian flux through a fixed curve segment naturally gives rise to the notion of a donating region, a compact point set in which each particle will pass through the curve and contribute to the flux. A precise geometric determination of the donating region has not been available until now. The author proposes an explicit, constructive, and analytical definition of the donating region based on two characteristic curves of the flow field, viz. streaklines and timelines. It is also shown that, within a time interval of finite size, each particle in the proposed donating region has a net effect of going across the fixed curve once. The presented analysis might be potentially useful for flow topology studies, Lagrangian flux calculation, and explicit interface tracking