Geodesic
The implementation of immersed boundary method for simulation of external flow on unstructured meshes
Matematičeskoe modelirovanie, Tome 27 (2015) no. 10, pp. 5-20.

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Based on immersed boundary conditions we build the numerical method of simulation of external flows around solid bodies on unstructured meshes. Two types of boundary conditions on the body surfase are implemented using different modifications of the method. The method efficiency is demonstrated on 2D model problems on subsonic and supersonic flow around a cylinder.
Keywords: numerical modeling, viscous flow, immersed boundary method, Brinkman penalization method, characteristic based volume penalization method. 
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I. V. Abalakin; N. S. Zhdanova; T. K. Kozubskaya. The implementation of immersed boundary method for simulation of external flow on unstructured meshes. Matematičeskoe modelirovanie, Tome 27 (2015) no. 10, pp. 5-20. http://geodesic.mathdoc.fr/item/MM_2015_27_10_a1/

[1] R. Mittal, G. Iaccarino, “Immersed boundary Methods”, Annu. Rev. Fluid Mech., 37 (2005), 239–261 | DOI | MR | Zbl

[2] C. S. Peskin, “Flow patterns around heart valves: a numerical method”, J. Comput. Phys., 10:2 (1972), 252–271 | DOI | MR | Zbl

[3] I. S. Menshov, M. A. Kornev, “Free-boundary method for the numerical solution of gas-dynamic equations in domains with varying geometry”, Mathematical Models and Computer Simulations, 6:6 (2014), 612–621 | DOI | MR | Zbl

[4] O. Boiron, G. Chiavassa, R. Donat, “A high-resolution penalization method for large Mach number flows in the presence of obstacles”, Computers and Fluids, 38:3 (2009), 703–714 | DOI | MR | Zbl

[5] E. Brown-Dymkoski, N. Kasimov, O. V. Vasilyev, “A characteristic based volume penalization method for general evolution problems applied to compressible viscous flows”, J. Comput. Phys., 262 (2014), 344–357 | DOI | MR

[6] E. Feireisl, J. Neustupa, J. Stebel, “Convergence of a Brinkman-type penalization for compressible fluid flows”, J. Differential Equations, 250:1 (2011), 596–606 | DOI | MR | Zbl

[7] S. Osher, R. Fedkiw, Level Set Methods and Dynamic Implicit Surfaces, Springer, New-York, 2003, 273 pp. | MR | Zbl

[8] I. V. Abalakin, P. A. Bakhvalov, A. V. Gorobets, A. P. Duben, T. K. Kozubskaia, “Parallelnyi programmnyi kompleks NOISETTE dlia krupnomasshtabnykh raschetov zadach aerodinamiki i aeroakustiki”, Vychislitelnye metody i programmirovanie, 13 (2012), 110–125 | MR

[9] I. V. Abalakin, T. K. Kozubskaia, “Skhema na osnove reberno-orientirovannoi kvaziodnomernoi rekonstruktsii peremennykh dlia resheniia zadach aerodinamiki i aeroakustiki na nestrukturirovannykh setkakh”, Matematicheskoe modelirovanie, 25:8 (2013), 109–136 | MR

[10] I. Abalakin, P. Bakhvalov, T. Kozubskaya, “Edge-based reconstruction schemes for prediction of near field flow region in complex aeroacoustics problems”, International Journal of Aeroacoustics, 13:3–4 (2014), 207–234

[11] M. Bergmann, A. Iollo, “Modeling and simulation of fish-like swimming”, J. Comput. Phys., 230:2 (2011), 329–348 | DOI | MR | Zbl

[12] R. D. Henderson, “Nonlinear dynamics and pattern formation in turbulent wake transition”, J. Fluid Mech., 352 (1997), 65–112 | DOI | MR | Zbl

[13] I. V. Abalakin, A. V. Gorobets, N. S. Zhdanova, T. K. Kozubskaia, “Primenenie metoda Brinkmana shtrafnykh funktsii dlia chislennogo modelirovaniia obtekaniia prepiatstvii viazkim szhimaemym gazom”, Keldysh Institute preprints, 2014, 011, 14 pp. | Zbl

[14] I. V. Abalakin, N. S. Zhdanova, T. K. Kozubskaia, “Immersed boundary method as applied to the simulation of external aerodynamics problems with various boundary conditions”, Doklady Mathematics, 91:2 (2015), 178–181 | DOI | DOI | Zbl