Volume 52, Issue 3
A Semi-Langrangian Vortex Penalization Method for 3D Incompressible Flows

Chlo Mimeau, Iraj Mortazavi & Georges-Henri Cottet

J. Math. Study, 52 (2019), pp. 277-298.

Published online: 2019-09

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  • Abstract

A remeshed Vortex method is proposed in this work to simulate threedimensional incompressible flows. The convection equation is solved on particles, using a Vortex method, which are then remeshed on a Cartesian underlying grid. The other differential operators involved in the governing incompressible Navier-Stokes equations are discretized on the grid, through finite differences method or in spectral space. In the present work, the redistribution of the particles on the Cartesian mesh is performed using a directional splitting, allowing to save significant computational efforts especially in the case of 3D flows. A coupling of this semi-Lagrangian method with an immersed boundary method, namely the Brinkman penalization technique, is proposed in this paper in order to efficiently take into account the presence of solid and porous obstacles in the fluid flow and then to perform passive flow control using porous medium. This method, which combines the robustness of particle methods and the flexibility of penalization method, is validated and exploited in the context of different flow physics.

  • Keywords

Semi-Lagrangian method, remeshed Vortex method, penalization approach, bluff body flows, DNS.

  • AMS Subject Headings

65M22, 35Q30, 76S05

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

chloe.mimeau@cnam.fr (Chlo Mimeau)

iraj.mortazavi@cnam.fr (Iraj Mortazavi)

georges-henri.cottet@univ-grenoble-alpes.fr (Georges-Henri Cottet)

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@Article{JMS-52-277, author = {Mimeau , Chlo and Mortazavi , Iraj and Cottet , Georges-Henri }, title = {A Semi-Langrangian Vortex Penalization Method for 3D Incompressible Flows}, journal = {Journal of Mathematical Study}, year = {2019}, volume = {52}, number = {3}, pages = {277--298}, abstract = {

A remeshed Vortex method is proposed in this work to simulate threedimensional incompressible flows. The convection equation is solved on particles, using a Vortex method, which are then remeshed on a Cartesian underlying grid. The other differential operators involved in the governing incompressible Navier-Stokes equations are discretized on the grid, through finite differences method or in spectral space. In the present work, the redistribution of the particles on the Cartesian mesh is performed using a directional splitting, allowing to save significant computational efforts especially in the case of 3D flows. A coupling of this semi-Lagrangian method with an immersed boundary method, namely the Brinkman penalization technique, is proposed in this paper in order to efficiently take into account the presence of solid and porous obstacles in the fluid flow and then to perform passive flow control using porous medium. This method, which combines the robustness of particle methods and the flexibility of penalization method, is validated and exploited in the context of different flow physics.

}, issn = {2617-8702}, doi = {https://doi.org/10.4208/jms.v52n3.19.04}, url = {http://global-sci.org/intro/article_detail/jms/13299.html} }
TY - JOUR T1 - A Semi-Langrangian Vortex Penalization Method for 3D Incompressible Flows AU - Mimeau , Chlo AU - Mortazavi , Iraj AU - Cottet , Georges-Henri JO - Journal of Mathematical Study VL - 3 SP - 277 EP - 298 PY - 2019 DA - 2019/09 SN - 52 DO - http://doi.org/10.4208/jms.v52n3.19.04 UR - https://global-sci.org/intro/article_detail/jms/13299.html KW - Semi-Lagrangian method, remeshed Vortex method, penalization approach, bluff body flows, DNS. AB -

A remeshed Vortex method is proposed in this work to simulate threedimensional incompressible flows. The convection equation is solved on particles, using a Vortex method, which are then remeshed on a Cartesian underlying grid. The other differential operators involved in the governing incompressible Navier-Stokes equations are discretized on the grid, through finite differences method or in spectral space. In the present work, the redistribution of the particles on the Cartesian mesh is performed using a directional splitting, allowing to save significant computational efforts especially in the case of 3D flows. A coupling of this semi-Lagrangian method with an immersed boundary method, namely the Brinkman penalization technique, is proposed in this paper in order to efficiently take into account the presence of solid and porous obstacles in the fluid flow and then to perform passive flow control using porous medium. This method, which combines the robustness of particle methods and the flexibility of penalization method, is validated and exploited in the context of different flow physics.

Chlo Mimeau , Iraj Mortazavi & Georges-Henri Cottet . (2019). A Semi-Langrangian Vortex Penalization Method for 3D Incompressible Flows. Journal of Mathematical Study. 52 (3). 277-298. doi:10.4208/jms.v52n3.19.04
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