Skip to main content Accessibility help
×
Home

An Accurate Cartesian Method for Incompressible Flows with Moving Boundaries

  • M. Bergmann (a1), J. Hovnanian (a1) and A. Iollo (a1)

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.

Copyright

Corresponding author

References

Hide All
[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.
[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.
[3]Bergmann, M. and Iollo, A., Modeling and simulation of fish-like swimming, J. Comput. Phys., 230 (2011), 329348.
[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).
[5]Chorin, A., Numerical solution of the Navier Stokes equations, Math. Comput., 22 (1968), 746762.
[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.
[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.
[8]Dehkordi, D., Moghaddam, H. and Jafari, H., Numerical simualtion of flow over two circular cylinders in tandem arrangement, J. Hydrodyn., 23 (2011), 114126.
[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.
[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.
[11]Ghias, R., Mittal, R. and Dong, H., A sharp interface immersed boundary method for compressible viscous flows, J. Comput. Phys., 225 (2007), 528553.
[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.
[13]Henderson, R., Details of the drag curve near the onset of vortex shedding, Phys. Fluids, 7 (1995), 21022104.
[14]Jin, G. and Braza, M., A nonreflecting outlet boundary condition for incompressible unsteady Navier-Stokes calculations, J. Comput Phys., 107(2) (1993), 239253.
[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.
[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.
[17]Li, Z. and Lai, M., The immersed interface method for the navier stokes equations with singular forces, J. Comput. Phys., 171 (2001), 822842.
[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.
[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.
[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.
[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.
[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.
[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.
[24]Mittal, R. and Iaccarino, G., Immersed boundary methods, Annu. Rev. Fluid. Mech., (2005), 127.
[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.
[26]Osher, S. and Fedkiw, R., Level Set Methods and Dynamic Implicit Surfaces, Springer, 2003.
[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).
[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.
[29]Peskin, C., Flow patterns around the heart valves, J. Comput. Phys., 10 (1972), 252271.
[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.
[31]Sethian, J., A fast marching level set method for monotonically advancing fronts, Appl. Math., 93 (1996), 15911595.
[32]Sethian, J. A., Level Set Methods and Fast Marching Methods, Cambridge University Press, Cambridge, UK, 1999.
[33]Sethian, J. A., Evolution, implementation, and application of level set and fast marching methods for advancing fronts, J. Comput. Phys., 169 (2001), 503555.
[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.
[35]Slaouti, A. and Stansby, P., Flow around two circular cylinders by random-vortex method, J. Fluids Struct., 6(6) (1992), 641670.
[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.
[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.
[38]Tryggvason, G., Bunner, B., Esmaeeli, A. and Al-Rawahi, N., Computational of multiphase flows, Adv. Appl. Mech., 39 (2003), 91120.
[39]Wieselsberger, C., New data on the laws of fluid resistance, NACA TN, 84 (1922).
[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.

Keywords

An Accurate Cartesian Method for Incompressible Flows with Moving Boundaries

  • M. Bergmann (a1), J. Hovnanian (a1) and A. Iollo (a1)

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed