Simulation of moving boundaries interacting with compressible reacting flows using a second-order adaptive Cartesian cut-cell method.

*(English)*Zbl 1381.76266Summary: A high-order adaptive Cartesian cut-cell method, developed in the past by the authors [ibid. 321, 342–368 (2016; Zbl 1349.76370)] for simulation of compressible viscous flow over static embedded boundaries, is now extended for reacting flow simulations over moving interfaces. The main difficulty related to simulation of moving boundary problems using immersed boundary techniques is the loss of conservation of mass, momentum and energy during the transition of numerical grid cells from solid to fluid and vice versa. Gas phase reactions near solid boundaries can produce huge source terms to the governing equations, which if not properly treated for moving boundaries, can result in inaccuracies in numerical predictions. The small cell clustering algorithm proposed in our previous work is now extended to handle moving boundaries enforcing strict conservation. In addition, the cell clustering algorithm also preserves the smoothness of solution near moving surfaces. A second order Runge-Kutta scheme where the boundaries are allowed to change during the sub-time steps is employed. This scheme improves the time accuracy of the calculations when the body motion is driven by hydrodynamic forces. Simple one dimensional reacting and non-reacting studies of moving piston are first performed in order to demonstrate the accuracy of the proposed method. Results are then reported for flow past moving cylinders at subsonic and supersonic velocities in a viscous compressible flow and are compared with theoretical and previously available experimental data. The ability of the scheme to handle deforming boundaries and interaction of hydrodynamic forces with rigid body motion is demonstrated using different test cases. Finally, the method is applied to investigate the detonation initiation and stabilization mechanisms on a cylinder and a sphere, when they are launched into a detonable mixture. The effect of the filling pressure on the detonation stabilization mechanisms over a hyper-velocity sphere launched into a hydrogen-oxygen-argon mixture is studied and a qualitative comparison of the results with the experimental data are made. Results indicate that the current method is able to correctly reproduce the different regimes of combustion observed in the experiments. Through the various examples it is demonstrated that our method is robust and accurate for simulation of compressible viscous reacting flow problems with moving/deforming boundaries.

##### MSC:

76M25 | Other numerical methods (fluid mechanics) (MSC2010) |

76N15 | Gas dynamics (general theory) |

##### Keywords:

immersed boundary method; cut-cell; second order accuracy; reacting flow; moving boundaries; strict conservation
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\textit{B. Muralidharan} and \textit{S. Menon}, J. Comput. Phys. 357, 230--262 (2018; Zbl 1381.76266)

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##### References:

[1] | Muralidharan, B.; Menon, S., A high-order adaptive Cartesian cut-cell method for simulation of compressible viscous flow over immersed bodies, J. Comput. Phys., 321, 342-368, (2016) · Zbl 1349.76370 |

[2] | Kailasanath, K., Review of propulsion applications of detonation waves, AIAA J., 38, 9, 1698-1708, (2000) |

[3] | Donea, J.; Giulani, S.; Halleux, J. P., An arbitrary Lagrangian-Eulerian finite element method for transient dynamic fluid-structure interactions, Comput. Methods Appl. Mech. Eng., 33, 1-3, 689-723, (1982) · Zbl 0508.73063 |

[4] | Hughes, T. J.; Liu, W. K.; Zimmerman, T. K., Lagrangian-Eulerian finite element formulation for incompressible viscous flows, Comput. Methods Appl. Mech. Eng., 3, 329-349, (1981) · Zbl 0482.76039 |

[5] | Steger, J.; Dougherty, F.; Benek, J., A Chimera grid scheme, (Ghia, K. N., Advances in Grid Generation, ASME FED-5, (1983)), 59-69 |

[6] | Henshaw, W.; Schwendeman, D., Moving overlapping grids with adaptive mesh refinement for high-speed reactive and non-reactive flow, J. Comput. Phys., 216, 744-779, (2006) · Zbl 1220.76052 |

[7] | Yang, G.; Causon, D.; Ingram, D., Calculation of compressible flows about complex moving geometries using a three-dimensional Cartesian cut cell method, Int. J. Numer. Methods Fluids, 33, 1121-1151, (2000) · Zbl 0980.76052 |

[8] | Fadlun, E.; Verzicoo, R.; Orlandi, R.; Mohd-Yusof, J., Combined immersed-boundary finite-difference methods for three-dimensional complex flow simulations, J. Comput. Phys., 161, 35-60, (2000) · Zbl 0972.76073 |

[9] | Tseng, T.; Freziger, J., A ghost-cell immersed boundary method for flow in complex geometry, J. Comput. Phys., 192, 593-623, (2003) · Zbl 1047.76575 |

[10] | Pogorelov, A.; Meinke, M.; Schröder, W., Cut-cell method based large-eddy simulation of tip-leakage flow, Phys. Fluids, 27, (2015) |

[11] | Lee, J.; Kim, J.; Choi, H.; Yang, K. S., Sources of spurious force oscillations from an immersed boundary method for moving-body problems, J. Comput. Phys., 230, 7, 2677-2695, (2011) · Zbl 1316.76075 |

[12] | Zeng, X.; Farhat, C., A systematic approach for constructing high-order immersed boundary and ghost fluid methods for fluid-structure interaction problems, J. Comput. Phys., 231, 2892-2923, (2012) · Zbl 1426.76443 |

[13] | Sambasivan, S.; Kapahi, A.; Udaykumar, H., Simulation of high speed impact, penetration and fragmentation problems on locally refined Cartesian grids, J. Comput. Phys., (2017), in press · Zbl 1349.74376 |

[14] | Arienti, M.; Hung, P.; Morano, E.; Shepherd, J., A level set approach to eulerian-Lagrangian coupling, J. Comput. Phys., 185, 213-251, (2003) · Zbl 1047.76567 |

[15] | LeVeque, R.; Li, Z., The immersed interface method for elliptic equations with discontinuous coefficients and singular sources, SIAM J. Numer. Anal., 31, 4, 1019-1044, (1993) · Zbl 0811.65083 |

[16] | Udaykumar, H.; Mittal, R.; Rampunggoon, P.; Khanna, A., A sharp interface Cartesian grid method for simulating flows with complex moving boundaries, J. Comput. Phys., 174, 345-380, (2001) · Zbl 1106.76428 |

[17] | Schneiders, L.; Hartmann, D.; Meinke, M.; Schröder, W., An accurate moving boundary formulation in cut-cell methods, J. Comput. Phys., 235, 786-809, (2012) |

[18] | Seo, J.; Mittal, R., A sharp interface immersed boundary method with improved mass conservation and reduced spurious pressure oscillations, J. Comput. Phys., 230, 7347-7363, (2011) · Zbl 1408.76162 |

[19] | Chen, L.; Yu, Y.; Hou, G., Sharp-interface immersed boundary lattice Boltzmann method with reduced spurious-pressure oscillations for moving boundaries, Phys. Rev. E, 87, (2013) |

[20] | Lee, J.; You, D., An implicit ghost-cell immersed boundary method for simulations of moving body problems with control of spurious force oscillations, J. Comput. Phys., 233, 295-314, (2013) |

[21] | Bergmann, M.; Hovnanian, J.; Iollo, A., An accurate Cartesian method for incompressible flows with moving boundaries, Commun. Comput. Phys., 15, 5, 1266-1290, (2014) · Zbl 1373.76156 |

[22] | Mittal, R.; Dong, H.; Bozkurttas, M.; Najjar, F. M.; Vargas, A.; von Loebbecke, A., A versatile sharp interface immersed boundary method for incompressible flows with complex boundaries, J. Comput. Phys., 10, 4825-4852, (2008) · Zbl 1388.76263 |

[23] | Mittal, R.; Iaccarino, G., Immersed boundary methods, Annu. Rev. Fluid Mech., 37, 239-261, (2005) · Zbl 1117.76049 |

[24] | Schneiders, L.; Günther, C.; Meinke, M.; Schröder, W., An efficient conservative cut-cell method for rigid bodies interacting with viscous compressible flows, J. Comput. Phys., 311, 62-86, (2016) · Zbl 1349.74345 |

[25] | Hartmann, D.; Meinke, M.; Schröder, W., A strictly conservative Cartesian cut-cell method for compressible viscous flows on adaptive grids, Comput. Methods Appl. Mech. Eng., 200, 1038-1052, (2011) · Zbl 1225.76211 |

[26] | Pember, R.; Bell, J.; Collela, P.; Crutchfield, W. Y.; Welcome, M. L., An adaptive Cartesian grid method for unsteady compressible flow in irregular regions, J. Comput. Phys., 120, 278-304, (1995) · Zbl 0842.76056 |

[27] | P. Colella, D. Graves, T. Ligocki, D. Martin, D. Modiano, D. Serafini, B. Van Straalen, Chombo software package for AMR applications-design document, 2000. |

[28] | Toro, E., Riemann solvers and numerical methods for fluid mechanics, (2009), Springer |

[29] | Ivan, L.; Groth, C., High-order solution-adaptive central essentially non-oscillatory (CENO) method for viscous flows, J. Comput. Phys., 257, Part A, 830-862, (2014) · Zbl 1349.76341 |

[30] | Genin, F.; Menon, S., Studies of shock/turbulent shear layer interaction using large-eddy simulation, Comput. Fluids, 39, 800-819, (2010) · Zbl 1242.76063 |

[31] | CCSE, Boxlib user guide, (2012), Center for Computational Sciences and Engineering, Tech. Rep. |

[32] | Browne, S.; Ziegler, J.; Shepherd, J. E., Numerical solution methods for shock and detonation jump conditions, (2015), GALCIT Report FM2006.006 |

[33] | Forrer, H.; Berger, M., Flow simulations on Cartesian grids involving complex moving geometries flows, Int. Ser. Numer. Math., 129, 315-324, (1998) · Zbl 0936.76040 |

[34] | Ye, T.; Mittal, R.; Udaykumar, H.; Shyy, W., An accurate Cartesian grid method for viscous incompressible flows with complex immersed boundaries, J. Comput. Phys., 156, 209-240, (1999) · Zbl 0957.76043 |

[35] | Liu, C.; Hu, C., An efficient immersed boundary treatment for complex moving object, J. Comput. Phys., 274, 654-680, (2014) · Zbl 1351.76169 |

[36] | Bouchon, F.; Dubois, T.; James, N., A second-order cut-cell method for the numerical simulation of 2D flows past obstacles, Comput. Fluids, 65, 80-91, (2012) · Zbl 1365.76186 |

[37] | Liepmann, H. W.; Roshko, A., Elements of gas dynamics, (1957), John Wiley and Sons · Zbl 0078.39901 |

[38] | Murman, S. M.; Aftosmis, M. J.; Berger, M. J., Implicit approaches for moving boundaries in a 3d Cartesian method, (41st Aerospace Sciences Meeting and Exhibit, Reno, Nevada, (2003)), AIAA paper AIAA-2003-1119 |

[39] | Kim, C.-S., An immersed-boundary finite volume method for simulations of flow in complex geometries, J. Comput. Phys., 171, 132-150, (2001) · Zbl 1057.76039 |

[40] | Tritton, D., Experiments on flow past a circular cylinder at low Reynolds numbers, J. Fluid Mech., 6, 547-567, (1959) · Zbl 0092.19502 |

[41] | McCarthy, J.; Kubota, T., A study of wakes behind a circular cylinder at m = 5.7, AIAA J., 2, 620-636, (1964) · Zbl 0117.43101 |

[42] | Billig, F. S., Shock-wave shapes around spherical and cylindrical-nosed bodies, J. Spacecr., 4, 6, 822-823, (1967) |

[43] | Guilmineau, E.; Queutey, P., A numerical simulation of vortex shedding from an oscillating circular cylinder, J. Fluids Struct., 16, 6, 773-794, (2002) |

[44] | Al-Marouf, M.; Samtaney, R., A versatile embedded boundary adaptive mesh method for compressible flow in complex geometry, J. Comput. Phys., 337, 339-378, (2017) |

[45] | Yang, J.; Balaras, E., An embedded-boundary formulation for large-eddy simulation of turbulent flows interacting with moving boundaries, J. Comput. Phys., 215, 1, 12-40, (2006) · Zbl 1140.76355 |

[46] | Bdzil, J.; Kapila, A., Shock-to-detonation transition: a model problem, Phys. Fluids, 4, 409-418, (1992) · Zbl 0744.76073 |

[47] | Dold, J.; Kapila, A., Comparison between shock initiations of detonation using thermally-sensitive and chain-branching chemical models, Combust. Flame, 85, 185-194, (1991) |

[48] | Sharpe, G., Numerical simulations of pulsating detonations: II. piston initiated detonations, Combust. Theory Model., 5, 623-638, (2001) · Zbl 1160.76427 |

[49] | Brown, C. J.; Thomas, G. O., Experimental studies of shock-induced ignition and transition to detonation in ethylene and propylene mixtures, Combust. Flame, 117, 861-870, (1999) |

[50] | Dieterding, R., Parallel adaptive simulation of multi-dimensional detonation structures, PhD Thesis, (2003) |

[51] | A.K. Kapila, D.W. Schwendeman, Detonation initiation modeling computation and mechanisms, in: ICHMT, Int. Symp. Adv. in Comp. Heat Transfer, April 19-24, 2004, Norway (CHT-04-C2). |

[52] | Jiang, Z.; Han, G.; Wang, C.; Zhang, F., Self-organized generation of transverse waves in diverging cylindrical detonations, Combust. Flame, 156, 1653-1661, (2009) |

[53] | Maeda, S.; Sumiya, S.; Kashara, J.; Matsuo, A., Scale effect of spherical projectiles for stabilization of oblique detonation waves, Shock Waves, 25, 141-150, (2015) |

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