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Research Article

Numerical modelling of shock–bubble interactions using a pressure-based algorithm without Riemann solvers

Fabian Denner( ), Berend G. M. van Wachem
Chair of Mechanical Process Engineering, Otto-von-Guericke-Universität Magdeburg, Universitätsplatz 2, 39106 Magdeburg, Germany
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Abstract

The interaction of a shock wave with a bubble features in many engineering and emerging technological applications, and has been used widely to test new numerical methods for compressible interfacial flows. Recently, density-based algorithms with pressure-correction methods as well as fully-coupled pressure-based algorithms have been established as promising alternatives to classical density-based algorithms based on Riemann solvers. The current paper investigates the predictive accuracy of fully-coupled pressure-based algorithms without Riemann solvers in modelling the interaction of shock waves with one-dimensional and two-dimensional bubbles in gas–gas and liquid–gas flows. For a gas bubble suspended in another gas, the mesh resolution and the applied advection schemes are found to only have a minor influence on the bubble shape and position, as well as the behaviour of the dominant shock waves and rarefaction fans. For a gas bubble suspended in a liquid, however, the mesh resolution has a critical influence on the shape, the position and the post-shock evolution of the bubble, as well as the pressure and temperature distribution.

Keywords

shock–bubble interactionshock capturinginterfacial flowsfinite-volume methodsvolume-of-fluid methods

References

 
Abgrall, R., Karni, S. 2001. Computations of compressible multifluids. J Comput Phys, 169: 594–623.
Crossref Google Scholar
 
Abgrall, R., Saurel, R. 2003. Discrete equations for physical and numerical compressible multiphase mixtures. J Comput Phys, 186: 361–396.
Crossref Google Scholar
 
Allaire, G., Clerc, S., Kokh, S. 2002. A five-equation model for the simulation of interfaces between compressible fluids. J Comput Phys, 181: 577–616.
Crossref Google Scholar
 
Anderson, J. D. 2003. Modern Compressible Flow: With a Historical Perspective. McGraw-Hill New York.
 
Ando, K., Liu, A.-Q., Ohl, C.-D. 2012. Homogeneous nucleation in water in microuidic channels. Phys Rev Lett, 109: 044501.
Crossref Google Scholar
 
Baer, M. R., Nunziato, J. W. 1986. A two-phase mixture theory for the deflagration-to-detonation transition (ddt) in reactive granular materials. Int J Multiphase Flow, 12: 861–889.
Crossref Google Scholar
 
Bagabir, A., Drikakis, D. 2001. Mach number effects on shock–bubble interaction. Shock Waves, 11: 209–218.
Crossref Google Scholar
 
Balay, S., Abhyankar, S., Adams, M. F., Brown, J., Brune, P., Buschelman, K., Dalcin, L. D., Eijkhout, V., Gropp, W., Kaushik, D., Knepley, M., May, D., McInnes, L. C., Munson, T., Rupp, K., Sanan, P., Smith, B., Zampini, S., Zhang, H., Zhang, H. 2017. PETSc users manual revision 3.8. Technical Report. ANL-95/11 - Revision 3.8. Argonne National Laboratory.
Crossref
 
Bartholomew, P., Denner, F., Abdol-Azis, M. H., Marquis, A., van Wachem, B. G. M. 2018. Unified formulation of the momentum-weighted interpolation for collocated variable arrangements. J Comput Phys, 375: 177–208.
Crossref Google Scholar
 
Bo, W., Grove, J. W. 2014. A volume of fluid method based ghost fluid method for compressible multi-fluid flows. Comput Fluid, 90: 113–122.
Crossref Google Scholar
 
Brouillette, M. 2002. The Richtmyer–Meshkov instability. Ann Rev Fluid Mech, 34: 445–468.
Crossref Google Scholar
 
Chang, C.-H., Liou, M.-S. 2007. A robust and accurate approach to computing compressible multiphase flow: Stratified flow model and AUSM+-up scheme. J Comput Phys, 225: 840–873.
Crossref Google Scholar
 
Chorin, A. J. 1967. A numerical method for solving incompressible viscous flow problems. J Comput Phys, 2: 12–26.
Crossref Google Scholar
 
Chorin, A. J., Marsden, J. E. 1993. A Mathematical Introduction to Fluid Mechanics. Springer Verlag.
Crossref
 
Coralic, V., Colonius, T. 2014. Finite-volume WENO scheme for viscous compressible multicomponent flows. J Comput Phys, 274: 95–121.
Crossref Google Scholar
 
Cordier, F., Degond, P., Kumbaro, A. 2012. An asymptotic-preserving all-speed scheme for the Euler and Navier–Stokes equations. J Comput Phys, 231: 5685–5704.
Crossref Google Scholar
 
Delale, C. F. 2013. Bubble Dynamics and Shock Waves. Springer Berlin Heidelberg.
Crossref
 
Demirdžić, I., Lilek, Ž., Perić, M. 1993. A collocated finite volume method for predicting flows at all speeds. Int J Numer Meth Fluids, 16: 1029–1050.
Crossref Google Scholar
 
Denner, F. 2018. Fully-coupled pressure-based algorithm for compressible flows: Linearisation and iterative solution strategies. Comput Fluid, 175: 53–65.
Crossref Google Scholar
 
Denner, F., van Wachem, B. 2015. TVD differencing on three-dimensional unstructured meshes with monotonicity-preserving correction of mesh skewness. J Comput Phys, 298: 466–479.
Crossref Google Scholar
 
Denner, F., van Wachem, B. G. M. 2014. Compressive VOF method with skewness correction to capture sharp interfaces on arbitrary meshes. J Comput Phys, 279: 127–144.
Crossref Google Scholar
 
Denner, F., Xiao, C.-N., van Wachem, B. G. M. 2018. Pressure-based algorithm for compressible interfacial flows with acoustically-conservative interface discretisation. J Comput Phys, 367: 192–234.
Crossref Google Scholar
 
Fedkiw, R. P., Aslam, T., Merriman, B., Osher, S. 1999a. A non-oscillatory eulerian approach to interfaces in multimaterial flows (the ghost fluid method). J Comput Phys, 152: 457–492.
Crossref Google Scholar
 
Fedkiw, R. P., Aslam, T., Xu, S. J. 1999b. The ghost fluid method for deflagration and detonation discontinuities. J Comput Phys, 154: 393–427.
Crossref Google Scholar
 
Fuster, D. 2018. A review of models for bubble clusters in cavitating flows. Flow Turbulence Combust, 102: 497–536.
Crossref Google Scholar
 
Fuster, D., Popinet, S. 2018. An all-Mach method for the simulation of bubble dynamics problems in the presence of surface tension. J Comput Phys, 374: 752–768
Crossref Google Scholar
 
Goncalves, E., Hoarau, Y., Zeidan, D. 2019. Simulation of shock-induced bubble collapse using a four-equation model. Shock Waves, 29: 221–234.
Crossref Google Scholar
 
Haas, J.-F., Sturtevant, B. 1987. Interaction of weak shock waves with cylindrical and spherical gas inhomogeneities. J Fluid Mech, 181: 41.
Crossref Google Scholar
 
Haimovich, O., Frankel, S. H. 2017. Numerical simulations of compressible multicomponent and multiphase flow using a high-order targeted ENO (TENO) finite-volume method. Comput Fluid, 146: 105–116.
Crossref Google Scholar
 
Harlow, F. H., Amsden, A. A. 1971a. A numerical fluid dynamics calculation method for all flow speeds. J Comput Phys, 8: 197–213.
Crossref Google Scholar
 
Harlow, F., Amsden, A. 1971b. Fluid Dynamics, Monograph LA-4700. Los Alamos National Laboratory.
 
Hauke, G., Hughes, T. J. R. 1998. A comparative study of different sets of variables for solving compressible and incompressible flows. Comput Method Appl M, 153: 1–44.
Crossref Google Scholar
 
Hejazialhosseini, B., Rossinelli, D., Koumoutsakos, P. 2013. Vortex dynamics in 3D shock–bubble interaction. Phys Fluid, 25: 110816.
Crossref Google Scholar
 
Hirt, C. W., Nichols, B. D. 1981. Volume of fluid (VOF) method for the dynamics of free boundaries. J Comput Phys, 39: 201–225.
Crossref Google Scholar
 
Hou, T. Y., Floch, P. G. L. 1994. Why nonconservative schemes converge to wrong solutions: Error analysis. Math Comput, 62: 497–530.
Crossref Google Scholar
 
Hu, X. Y., Khoo, B. C. 2004. An interface interaction method for compressible multifluids. J Comput Phys, 198: 35–64.
Crossref Google Scholar
 
Johnsen, E. 2007. Numerical simulations of non-spherical bubble collapse: With applications to shockwave lithotripsy. Ph.D. Thesis. California Institute of Technology, USA.
 
Johnsen, E. R. I. C., Colonius, T. I. M. 2009. Numerical simulations of non-spherical bubble collapse. J Fluid Mech, 629: 231–262.
Crossref Google Scholar
 
Johnsen, E., Colonius, T. 2006. Implementation of WENO schemes in compressible multicomponent flow problems. J Comput Phys, 219: 715–732.
Crossref Google Scholar
 
Karimian, S. M. H., Schneider, G. E. 1994. Pressure-based computational method for compressible and incompressible flows. J Thermophys Heat Tr, 8: 267–274.
Crossref Google Scholar
 
Kokh, S., Lagoutière, F. 2010. An anti-diffusive numerical scheme for the simulation of interfaces between compressible fluids by means of a five-equation model. J Comput Phys, 229: 2773–2809.
Crossref Google Scholar
 
Kunz, R. F., Cope, W. K., Venkateswaran, S. 1999. Development of an implicit method for multi-fluid flow simulations. J Comput Phys, 152: 78–101.
Crossref Google Scholar
 
Layes, G., Jourdan, G., Houas, L. 2003. Distortion of a spherical gaseous interface accelerated by a plane shock wave. Phys Rev Lett, 91: 174502.
Crossref Google Scholar
 
Layes, G., Jourdan, G., Houas, L. 2005. Experimental investigation of the shock wave interaction with a spherical gas inhomogeneity. Phys Fluid, 17: 028103.
Crossref Google Scholar
 
Liu, C., Hu, C. H. 2017. Adaptive THINC-GFM for compressible multi-medium flows. J Comput Phys, 342: 43–65.
Crossref Google Scholar
 
Liu, T. G., Khoo, B. C., Yeo, K. S. 2003. Ghost fluid method for strong shock impacting on material interface. J Comput Phys, 190: 651–681.
Crossref Google Scholar
 
Michael, L., Nikiforakis, N. 2019. The evolution of the temperature field during cavity collapse in liquid nitromethane. Part I: Inert case. Shock Waves, 29: 153–172.
Crossref Google Scholar
 
Moguen, Y., Bruel, P., Dick, E. 2015. Solving low Mach number Riemann problems by a momentum interpolation method. J Comput Phys, 298: 741–746.
Crossref Google Scholar
 
Moguen, Y., Bruel, P., Dick, E. 2019. A combined momentum-interpolation and advection upstream splitting pressure-correction algorithm for simulation of convective and acoustic transport at all levels of Mach number. J Comput Phys, 384: 16–41.
Crossref Google Scholar
 
Moguen, Y., Kousksou, T., Bruel, P., Vierendeels, J., Dick, E. 2012. Pressure–velocity coupling allowing acoustic calculation in low Mach number flow. J Comput Phys, 231: 5522–5541.
Crossref Google Scholar
 
Moukalled, F., Mangani, L., Darwish, M. 2016. The Finite Volume Method in Computational Fluid Dynamics: An Advanced Introduction with OpenFOAM and Matlab. Springer.
Crossref
 
Murrone, A., Guillard, H. 2005. A five equation reduced model for compressible two phase flow problems. J Comput Phys, 202: 664–698.
Crossref Google Scholar
 
Niederhaus, J. H. J., Greenough, J. A., Oakley, J. G., Bonazza, R. 2008a. Vorticity evolution in two- and three-dimensional simulations for shock–bubble interactions. Phys Scripta, T132: 014019.
Crossref Google Scholar
 
Niederhaus, J. H. J., Greenough, J. A., Oakley, J. G., Ranjan, D., Anderson, M. H., Bonazza, R. 2008b. A computational parameter study for the three-dimensional shock–bubble interaction. J Fluid Mech, 594: 85–124.
Crossref Google Scholar
 
Nourgaliev, R. R., Dinh, T. N., Theofanous, T. G. 2006. Adaptive characteristics-based matching for compressible multifluid dynamics. J Comput Phys, 213: 500–529.
Crossref Google Scholar
 
Ohl, S.-W., Ohl, C.-D. 2016. Acoustic cavitation in a microchannel. In: Handbook of Ultrasonics and Sonochemistry. Springer Singapore, 99–135.
Crossref
 
Pan, S., Adami, S., Hu, X., Adams, N. A. 2018. Phenomenology of bubble-collapse-driven penetration of biomaterial-surrogate liquid–liquid interfaces. Phys Rev Fluids, 3: 114005.
Crossref Google Scholar
 
Park, J. H., Munz, C.-D. 2005. Multiple pressure variables methods for fluid flow at all Mach numbers. Int J Numer Meth Fluids, 49: 905–931.
Crossref Google Scholar
 
Quirk, J. J., Karni, S. 1996. On the dynamics of a shock–bubble interaction. J Fluid Mech, 318: 129.
Crossref Google Scholar
 
Ranjan, D., Niederhaus, J., Motl, B., Anderson, M., Oakley, J., Bonazza, R. 2007. Experimental investigation of primary and secondary features in high-Mach-number shock-bubble interaction. Phys Rev Lett, 98: 024502.
Crossref Google Scholar
 
Ranjan, D., Oakley, J., Bonazza, R. 2011. Shock–bubble interactions. Annu Rev Fluid Mech, 43: 117–140.
Crossref Google Scholar
 
Roe, P. 1986. Characteristic-based schemes for the Euler equations. Ann Rev Fluid Mech, 18: 337–365.
Crossref Google Scholar
 
Saurel, R., Abgrall, R. 1999. A simple method for compressible multifluid flows. SIAM J Sci Comput, 21: 1115–1145.
Crossref Google Scholar
 
Saurel, R., Le Métayer, O., Massoni, J., Gavrilyuk, S. 2007. Shock jump relations for multiphase mixtures with stiff mechanical relaxation. Shock Waves, 16: 209–232.
Crossref Google Scholar
 
Saurel, R., Pantano, C. 2018. Diffuse-interface capturing methods for compressible two-phase flows. Ann Rev Fluid Mech, 50: 105–130.
Crossref Google Scholar
 
Shukla, R. K. 2014. Nonlinear preconditioning for efficient and accurate interface capturing in simulation of multicomponent compressible flows. J Comput Phys, 276: 508–540.
Crossref Google Scholar
 
Shukla, R. K., Pantano, C., Freund, J. B. 2010. An interface capturing method for the simulation of multi-phase compressible flows. J Comput Phys, 229: 7411–7439.
Crossref Google Scholar
 
Shyue, K.-M. 2006. A volume-fraction based algorithm for hybrid barotropic and non-barotropic two-fluid flow problems. Shock Waves, 15: 407–423.
Crossref Google Scholar
 
Terashima, H., Tryggvason, G. 2009. A front-tracking/ghost-fluid method for fluid interfaces in compressible flows. J Comput Phys, 228: 4012–4037.
Crossref Google Scholar
 
Tian, B. L., Toro, E. F., Castro, C. E. 2011. A path-conservative method for a five-equation model of two-phase flow with an HLLC-type Riemann solver. Comput Fluid, 46: 122–132.
Crossref Google Scholar
 
Tokareva, S. A., Toro, E. F. 2010. HLLC-type Riemann solver for the Baer–Nunziato equations of compressible two-phase flow. J Comput Phys, 229: 3573–3604.
Crossref Google Scholar
 
Toro, E. F., Spruce, M., Speares, W. 1994. Restoration of the contact surface in the HLL-Riemann solver. Shock Waves, 4: 25–34.
Crossref Google Scholar
 
Turkel, E. 2006. Numerical methods and nature. J Sci Comput, 28: 549–570.
Crossref Google Scholar
 
Turkel, E., Fiterman, A., van Leer, B. 1993. Preconditioning and the limit to the incompressible flow equations. Technical Report. NASA CR-191500. Institute for Computer Applications in Science and Engineering Hampton VA, USA.
 
Ubbink, O., Issa, R. I. 1999. A method for capturing sharp fluid interfaces on arbitrary meshes. J Comput Phys, 153: 26–50.
Crossref Google Scholar
 
Van der Heul, D. R., Vuik, C., Wesseling, P. 2003. A conservative pressure-correction method for flow at all speeds. Comput Fluid, 32: 1113–1132.
Crossref Google Scholar
 
Van Doormaal, J. P., Raithby, G. D., McDonald, B. H. 1987. The segregated approach to predicting viscous compressible fluid flows. J Turbomach, 109: 268–277.
Crossref Google Scholar
 
Wang, C. W., Liu, T. G., Khoo, B. C. 2006. A real ghost fluid method for the simulation of multimedium compressible flow. SIAM J Sci Comput, 28: 278–302.
Crossref Google Scholar
 
Wesseling, P. 2001. Principles of Computational Fluid Dynamics. Springer.
Crossref
 
Wong, M. L., Lele, S. K. 2017. High-order localized dissipation weighted compact nonlinear scheme for shock- and interface-capturing in compressible flows. J Comput Phys, 339: 179–209.
Crossref Google Scholar
 
Xiang, G., Wang, B. 2017. Numerical study of a planar shock interacting with a cylindrical water column embedded with an air cavity. J Fluid Mech, 825: 825–852.
Crossref Google Scholar
 
Xiao, C.-N., Denner, F., van Wachem, B. G. M. 2017. Fully-coupled pressure-based finite-volume framework for the simulation of fluid flows at all speeds in complex geometries. J Comput Phys, 346: 91–130.
Crossref Google Scholar
 
Xiao, F. 2004. Unified formulation for compressible and incompressible flows by using multi-integrated moments I: One-dimensional inviscid compressible flow. J Comput Phys, 195: 629–654.
Crossref Google Scholar
 
Yoo, Y.-L., Sung, H.-G. 2018. Numerical investigation of an interaction between shock waves and bubble in a compressible multiphase flow using a diffuse interface method. Int J Heat Mass Tran, 127: 210–221.
Crossref Google Scholar
 
Zhai, Z., Si, T., Luo, X., Yang, J. 2011. On the evolution of spherical gas interfaces accelerated by a planar shock wave. Phys Fluid, 23: 084104.
Crossref Google Scholar
Experimental and Computational Multiphase Flow
Volume 1 Issue 4,
December 2019
Pages 271-285
DOI: 10.1007/s42757-019-0021-2
Cite this article:
Denner F, van Wachem BGM. Numerical modelling of shock–bubble interactions using a pressure-based algorithm without Riemann solvers. Experimental and Computational Multiphase Flow, 2019, 1(4): 271-285. https://doi.org/10.1007/s42757-019-0021-2

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Received: 26 February 2019
Revised: 02 April 2019
Accepted: 03 April 2019
Published: 05 December 2019
© Tsinghua University Press 2019
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