Skip to main content Accessibility help
×
Home
Hostname: page-component-568f69f84b-l2zqg Total loading time: 0.22 Render date: 2021-09-16T17:07:28.248Z Has data issue: true Feature Flags: { "shouldUseShareProductTool": true, "shouldUseHypothesis": true, "isUnsiloEnabled": true, "metricsAbstractViews": false, "figures": true, "newCiteModal": false, "newCitedByModal": true, "newEcommerce": true, "newUsageEvents": true }

An Accurate Cartesian Method for Incompressible Flows with Moving Boundaries

Published online by Cambridge University Press:  03 June 2015

M. Bergmann*
Affiliation:
Inria, F-33400 Talence, France, Univ. Bordeaux, 1MB, UMR 5251, F-33400 Talence, France, CNRS, 1MB, UMR 5251, F-33400 Talence, France
J. Hovnanian*
Affiliation:
Inria, F-33400 Talence, France, Univ. Bordeaux, 1MB, UMR 5251, F-33400 Talence, France, CNRS, 1MB, UMR 5251, F-33400 Talence, France
A. Iollo*
Affiliation:
Inria, F-33400 Talence, France, Univ. Bordeaux, 1MB, UMR 5251, F-33400 Talence, France, CNRS, 1MB, UMR 5251, F-33400 Talence, France
*Corresponding
Get access

Abstract

An accurate cartesian method is devised to simulate incompressible viscous flows past an arbitrary moving body. The Navier-Stokes equations are spatially discretized onto a fixed Cartesian mesh. The body is taken into account via the ghost-cell method and the so-called penalty method, resulting in second-order accuracy in velocity. The accuracy and the efficiency of the solver are tested through two-dimensional reference simulations. To show the versatility of this scheme we simulate a three-dimensional self propelled jellyfish prototype.

Type
Research Article
Copyright
Copyright © Global Science Press Limited 2014

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1]Angot, P., Bruneau, C. H. and Fabrie, P., A penalization method to take into account obstacles in incompressible flows, Numer. Math., 81(4) (1999), 497520.CrossRefGoogle Scholar
[2]Bergmann, M., Optimisation Aérodynamique par Réduction de Modele POD et Contrle Optimal, Application au Sillage Laminaire D’un Cylindre Circulaire, PhD thesis, Institut National Polytechnique de Lorraine, 2004.Google Scholar
[3]Bergmann, M. and Iollo, A., Modeling and simulation of fish-like swimming, J. Comput. Phys., 230 (2011), 329348.CrossRefGoogle Scholar
[4]Braza, M., Chassaing, P. and Minh, H. H., Numerical study and physical analysis of the pressure and velocity fields in the near wake of a circular cylinder, J. Fluid. Mech., 165 (1986).CrossRefGoogle Scholar
[5]Chorin, A., Numerical solution of the Navier Stokes equations, Math. Comput., 22 (1968), 746762.CrossRefGoogle Scholar
[6]Coquerelle, M. and Cottet, G. H., A vortex level set method for the two-way coupling of an incompressible fluid with colliding rigid bodies, J. Comput. Phys., 227(21) (2008), 91219137.CrossRefGoogle Scholar
[7]Dabiri, J., Colin, S., Costello, J. and Gharib, M., Flow patterns generated by oblate medusan jellyfish: field measurements and laboratory analyses, J. Experimental Bio., 208 (2005), 1257–1265.CrossRefGoogle ScholarPubMed
[8]Dehkordi, D., Moghaddam, H. and Jafari, H., Numerical simualtion of flow over two circular cylinders in tandem arrangement, J. Hydrodyn., 23 (2011), 114126.CrossRefGoogle Scholar
[9]Ding, H., Shu, C. and Yeo, K., Numerical simulation of flows around two circular cylonders by mesh-free least square-based finite difference methods, Int. J. Numer. Meth. Fluids, 53 (2007), 305332.CrossRefGoogle Scholar
[10]Duarte, F., Gormaz, R. and Natesan, S., Arbitrary lagrangian-eulerian method for navier stokes equations with moving boundaries, Comput. Methods Appl. Math. Eng., 193 (2004), 48194836.CrossRefGoogle Scholar
[11]Ghias, R., Mittal, R. and Dong, H., A sharp interface immersed boundary method for compressible viscous flows, J. Comput. Phys., 225 (2007), 528553.CrossRefGoogle Scholar
[12]Gibou, F., Fedkiw, R., Cheng, L. and Kang, M., A second order accurate symmetric discretization of the poisson equation on irregular domains, J. Comput. Phys., 176 (2002), 205227.CrossRefGoogle Scholar
[13]Henderson, R., Details of the drag curve near the onset of vortex shedding, Phys. Fluids, 7 (1995), 21022104.CrossRefGoogle Scholar
[14]Jin, G. and Braza, M., A nonreflecting outlet boundary condition for incompressible unsteady Navier-Stokes calculations, J. Comput Phys., 107(2) (1993), 239253.CrossRefGoogle Scholar
[15]Koumoutsakos, P. and Leonard, A., High-resolution simulations of the flow around an impulsively started cylinder using vortex methods, J. Fluid Mech., 296 (1995), 138.CrossRefGoogle Scholar
[16]Lee, J., Kim, J., Choi, H. and Yang, K. S., Sources of spurious force oscillations from an immersed boundary method for moving-body problems, J. Comput. Phys., 230(7) (2011), 2677–2695.CrossRefGoogle Scholar
[17]Li, Z. and Lai, M., The immersed interface method for the navier stokes equations with singular forces, J. Comput. Phys., 171 (2001), 822842.CrossRefGoogle Scholar
[18]Liao, C. C., Chang, Y. W., Lin, C. A. and McDonough, J. M., Simulating flows with moving rigid boundary using immersed-boundary method, Comput. Fluids, 39(1) (2010), 152167.CrossRefGoogle Scholar
[19]Liu, H., Krishnan, S., Marella, S. and Udaykumar, H., Sharp interface castesian grid method ii: a technique fir simulationg droplet interactions with surfaces of arbitrary shape, J. Comput. Phys., 210 (2005), 3254.CrossRefGoogle Scholar
[20]Mahir, N. and Altac, Z., Numerical investigation of convective heat transfer in unsteady flow past two cylinders in tandem arrangements, Int. J. Heat Fluid Flow, 29 (2008), 13091318.CrossRefGoogle Scholar
[21]Marella, S., Krishnan, S., Liu, H. and Udaykumar, H., Sharp interface cartesian grid method i: an easily implemented technique for 3d moving boundary computations, J. Comput. Phys., 210 (2005), 131.CrossRefGoogle Scholar
[22]Meneghini, J. and Satara, F., Numerical simulation of flow interference between two cylinders in tandem and side-by-side arrangements, J. Fluids Struct., 15 (2001), 327350.CrossRefGoogle Scholar
[23]Mittal, R., Dong, H., Bozkurttas, M., Najjar, F., Vargas, A. and Loebbecke, A. von, A versatile sharp interface immersed boundary method for incompressible flows with complex boundaries, J. Comput. Phys., 227 (2008), 48254852.CrossRefGoogle ScholarPubMed
[24]Mittal, R. and Iaccarino, G., Immersed boundary methods, Annu. Rev. Fluid. Mech., (2005), 127.Google Scholar
[25]Mittal, S., Kumar, V. and Raghuvanshi, A., Unsteady incompressible flows past two cylinders in tandem and staggered arrangements, Int. J. Numer. Meth. Fluids, 25 (1997), 13151344.3.0.CO;2-P>CrossRefGoogle Scholar
[26]Osher, S. and Fedkiw, R., Level Set Methods and Dynamic Implicit Surfaces, Springer, 2003.CrossRefGoogle Scholar
[27]Osher, S. and Sethian, J. A., Fronts propagating with curvature-dependent speed: algorithms based on hamilton-jacobi formulations, J. Comput. Phys., 79(12) (1988).CrossRefGoogle Scholar
[28]Ploumhans, P. G. W., Vortex methods for high-resolution simulations of viscous flow past bluff bodies in general geometry, J. Comput. Phys., 165 (2000), 354406.CrossRefGoogle Scholar
[29]Peskin, C., Flow patterns around the heart valves, J. Comput. Phys., 10 (1972), 252271.CrossRefGoogle Scholar
[30]Seo, J. H. and Mittal, R., A sharp-interface immersed boundary method with improved mass conservation and reduced spurious pressure oscillations, J. Comput. Phys., 230(19) (2011), 73477363.CrossRefGoogle ScholarPubMed
[31]Sethian, J., A fast marching level set method for monotonically advancing fronts, Appl. Math., 93 (1996), 15911595.Google ScholarPubMed
[32]Sethian, J. A., Level Set Methods and Fast Marching Methods, Cambridge University Press, Cambridge, UK, 1999.Google Scholar
[33]Sethian, J. A., Evolution, implementation, and application of level set and fast marching methods for advancing fronts, J. Comput. Phys., 169 (2001), 503555.Google Scholar
[34]Sharman, B., Lien, F. and Davidson, L., Numerical predictions of low reynolds number flows over two tandem circular cylinders, Int. J. Numer. Meth. Fluids, 47(5) (2005), 423447.CrossRefGoogle Scholar
[35]Slaouti, A. and Stansby, P., Flow around two circular cylinders by random-vortex method, J. Fluids Struct., 6(6) (1992), 641670.CrossRefGoogle Scholar
[36]Sussman, M., Smereka, P. and Osher, S., A level set approach for computing solutions to incompressible 2-phade flow, J. Comput. Phys., 114 (1994), 146159.CrossRefGoogle Scholar
[37]Temam, R., Sur l’approximation de la solution deséquations denavier-stokes par la méthode des pas fractionnaires, Arch. Rational Mech. Anal., 32 (1969), 135153.CrossRefGoogle Scholar
[38]Tryggvason, G., Bunner, B., Esmaeeli, A. and Al-Rawahi, N., Computational of multiphase flows, Adv. Appl. Mech., 39 (2003), 91120.Google Scholar
[39]Wieselsberger, C., New data on the laws of fluid resistance, NACA TN, 84 (1922).Google Scholar
[40]Yang, Y. and Udaykumar, H., Sharp interface castesian grid method iii: solidification of pure materials and binary solutions, J. Comput. Phys., 210 (2005), 5574.CrossRefGoogle Scholar
12
Cited by

Send article to Kindle

To send this article to your Kindle, first ensure no-reply@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about sending to your Kindle. Find out more about sending to your Kindle.

Note you can select to send to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be sent to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

An Accurate Cartesian Method for Incompressible Flows with Moving Boundaries
Available formats
×

Send article to Dropbox

To send this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Dropbox.

An Accurate Cartesian Method for Incompressible Flows with Moving Boundaries
Available formats
×

Send article to Google Drive

To send this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Google Drive.

An Accurate Cartesian Method for Incompressible Flows with Moving Boundaries
Available formats
×
×

Reply to: Submit a response

Please enter your response.

Your details

Please enter a valid email address.

Conflicting interests

Do you have any conflicting interests? *