## A transfer operator based computational study of mixing processes in open flow systems

Publikation: Beiträge in Zeitschriften › Konferenzaufsätze in Fachzeitschriften › Forschung › begutachtet

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**A transfer operator based computational study of mixing processes in open flow systems.**/ Klünker, Anna; Padberg-Gehle, Kathrin.

in: Proceedings in applied mathematics and mechanics, Jahrgang 20, Nr. 1, e202000133, 25.01.2021.

Publikation: Beiträge in Zeitschriften › Konferenzaufsätze in Fachzeitschriften › Forschung › begutachtet

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*Proceedings in applied mathematics and mechanics*, Jg. 20, Nr. 1, e202000133. https://doi.org/10.1002/pamm.202000133

### APA

*Proceedings in applied mathematics and mechanics*,

*20*(1), Artikel e202000133. https://doi.org/10.1002/pamm.202000133

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### RIS

TY - JOUR

T1 - A transfer operator based computational study of mixing processes in open flow systems

AU - Klünker, Anna

AU - Padberg-Gehle, Kathrin

N1 - Conference code: 91

PY - 2021/1/25

Y1 - 2021/1/25

N2 - We study mixing by chaotic advection in open flow systems, where the corresponding small‐scale structures are created by means of the stretching and folding property of chaotic flows. The systems we consider contain an inlet and an outlet flow region as well as a mixing region and are characterized by constant in‐ and outflow of fluid particles. The evolution of a mass distribution in the open system is described via a transfer operator. The spatially discretized approximation of the transfer operator defines the transition matrix of an absorbing Markov chain restricted to finite transient states. We study the underlying mixing processes via this substochastic transition matrix. We conduct parameter studies for example systems with two differently colored fluids. We quantify the mixing of the resulting patterns by several mixing measures. In case of chaotic advection the transport processes in the open system are organized by the chaotic saddle and its stable and unstable manifolds. We extract these structures directly from leading eigenvectors of the transition matrix.

AB - We study mixing by chaotic advection in open flow systems, where the corresponding small‐scale structures are created by means of the stretching and folding property of chaotic flows. The systems we consider contain an inlet and an outlet flow region as well as a mixing region and are characterized by constant in‐ and outflow of fluid particles. The evolution of a mass distribution in the open system is described via a transfer operator. The spatially discretized approximation of the transfer operator defines the transition matrix of an absorbing Markov chain restricted to finite transient states. We study the underlying mixing processes via this substochastic transition matrix. We conduct parameter studies for example systems with two differently colored fluids. We quantify the mixing of the resulting patterns by several mixing measures. In case of chaotic advection the transport processes in the open system are organized by the chaotic saddle and its stable and unstable manifolds. We extract these structures directly from leading eigenvectors of the transition matrix.

KW - Mathematics

UR - https://www.mendeley.com/catalogue/ee694f5c-343a-39ea-bd62-b3917d83bce7/

U2 - 10.1002/pamm.202000133

DO - 10.1002/pamm.202000133

M3 - Conference article in journal

VL - 20

JO - Proceedings in applied mathematics and mechanics

JF - Proceedings in applied mathematics and mechanics

SN - 1617-7061

IS - 1

M1 - e202000133

T2 - 91st Annual Meeting of the International Association of Applied Mathematics and Mechanics - GAMM 2020

Y2 - 16 March 2020 through 20 March 2020

ER -