Compressible Multiphase Flow: Cavitation and Collapse Phenomena

Cloud Cavitation

Cavitation is encountered in liquid flows which are subject to large pressure variations. It refers to the rapid growth of vapor nuclei in low pressure regions followed by an intense collapse of the resulting vapor pockets in zones of high pressure. This process is known for its detrimental impact onto engineering devices. The caused effects comprise, among other things, material erosion, noise and vibrations and thus limit the lifetime of the affected device. In contrast, the power of caviation can also be harnessed, for instance, for biomedical applications, cleaning purposes or vegetable oil extraction.

On the one hand, attempts to make use of the destructive power of cavitation needs precise control of the behavior of only a few gas bubbles. On the other hand, the design of engineering devices requires accurate models that are able to predict the collective behavior of cavitating and potentially turbulent flow. The latter typically involves thousands of vapor bubbles and includes a multitude of spatio-temporal scales. A detailed understanding of these complex processes is a particularly challenging task which cannot be captured by experimental measurements only, but also requires numerical investigations.

We perfom large-scale simulations of clouds of tens of thousands gas bubbles that are subject to a collapse process. Systems with such a large number of bubbles are computationally enabled by Cubism-MPCF, an open-source compressible multicomponent flow solver for high performance computing, which is developed and maintained by the members of the CSElab. The software is available for download here.

Figure 1 shows a close up of the outer surface of a cloud comprising 50 000 bubbles. The bubbles first collapse at the outer surface of the cloud. This process comes along with the formation of micro jets due to bubble-bubble interactions. The combined effect of individual collapsing bubbles results in the formation of an inward-propagating pressure wave and velocity front. While moving towards the core of the cloud, the pressure wave and the velocity front continuously increase in strength. Eventually, significant pressure amplifications are observed in the core region.

Large-scale simulation of collapse process of spherical cloud with 50’000 bubbles.

Shock Induced Bubble Collapse

Further simulations consider shock induced collapses of arrays of bubbles. Figure 2 depicts a rendering of the pressure field and the air/liquid interface for a linear array of bubbles that are subject to an incoming shock from the left-hand side. The dense orange fields correspond to very high pressures while thin green fields corresponds to moderately high pressures.

Shock induced collapse of an array of ten bubbles. The image shows a volume rendering of pressure for a collapsing bubble in the middle of the array. Orange color denotes high pressure (2500 bar), green colors correspond to low pressure (800 bar).

People: Fabian Wermelinger, Petr Karnakov, Panos Hadjidoukas
Funding: ETH Zürich



  • U. Rasthofer, F. Wermelinger, P. Karnakov, J. Šukys, and P. Koumoutsakos, “Computational study of the collapse of a cloud with 12500 gas bubbles in a liquid,” Phys. Rev. Fluids, vol. 4, p. 63602, 2019.
    [BibTeX] [PDF] [DOI]
    author = {Rasthofer, U. and Wermelinger, F. and Karnakov, P. and {\v{S}}ukys, J. and Koumoutsakos, P.},
    doi = {10.1103/PhysRevFluids.4.063602},
    issue = {6},
    journal = {{Phys. Rev. Fluids}},
    month = {Jun},
    numpages = {30},
    pages = {063602},
    publisher = {American Physical Society},
    title = {Computational study of the collapse of a cloud with 12500 gas bubbles in a liquid},
    url = {},
    volume = {4},
    year = {2019}


  • F. Wermelinger, U. Rasthofer, P. E. Hadjidoukas, and P. Koumoutsakos, “Petascale simulations of compressible flows with interfaces,” J. Comput. Sci., vol. 26, p. 217–225, 2018.
    [BibTeX] [Abstract] [PDF] [DOI]

    We demonstrate a high throughput software for the efficient simulation of compressible multicomponent flow on high performance computing platforms. The discrete problem is represented on structured three-dimensional grids with non-uniform resolution. Discontinuous flow features are captured using a diffuse interface method. A distinguishing characteristic of the method is the proper treatment of the interface zone as a mixing region of liquid and gas. The governing equations are discretized by a Godunov-type finite volume method with explicit time stepping using a low-storage Runge-Kutta scheme. The presented flow solver Cubism-MPCF is based on our Cubism library which enables a highly optimized framework for the efficient treatment of stencil based problems on multicore architectures. The framework is general and not limited to applications in fluid dynamics. We validate our solver by classical benchmark examples. Furthermore, we examine a highly-resolved shock-induced bubble collapse and a cloud of O(10^3) collapsing bubbles, which demonstrate the high potential of the proposed framework and solver.

    author = {F. Wermelinger and U. Rasthofer and P.E. Hadjidoukas and P. Koumoutsakos},
    doi = {10.1016/j.jocs.2018.01.008},
    journal = {{J. Comput. Sci.}},
    month = {may},
    pages = {217--225},
    publisher = {Elsevier {BV}},
    title = {Petascale simulations of compressible flows with interfaces},
    url = {},
    volume = {26},
    year = {2018}


  • P. E. Hadjidoukas, D. Rossinelli, F. Wermelinger, J. Sukys, U. Rasthofer, C. Conti, B. Hejazialhosseini, and P. Koumoutsakos, “High throughput simulations of two-phase flows on Blue Gene/Q,” in Parallel computing: on the road to exascale – ParCo 2015, 2016, p. 767–776.
    [BibTeX] [PDF] [DOI]
    author = {Panagiotis E. Hadjidoukas and Diego Rossinelli and Fabian Wermelinger and Jonas Sukys and Ursula Rasthofer and Christian Conti and Babak Hejazialhosseini and Petros Koumoutsakos},
    booktitle = {Parallel Computing: On the Road to Exascale – {ParCo} 2015},
    doi = {10.3233/978-1-61499-621-7-767},
    note = {Proceedings of the International Conference on Parallel Computing – {ParCo} 2015},
    pages = {767--776},
    publisher = {{IOS} Press},
    series = {Advances in Parallel Computing},
    title = {High throughput simulations of two-phase flows on {Blue Gene/Q}},
    url = {},
    volume = {27},
    year = {2016}

  • F. Wermelinger, B. Hejazialhosseini, P. Hadjidoukas, D. Rossinelli, and P. Koumoutsakos, “An efficient compressible multicomponent flow solver for heterogeneous CPU/GPU architectures,” in Proceedings of the platform for advanced scientific computing – PASC ’16, 2016.
    [BibTeX] [PDF] [DOI]
    author = {Fabian Wermelinger and Babak Hejazialhosseini and Panagiotis Hadjidoukas and Diego Rossinelli and Petros Koumoutsakos},
    booktitle = {Proceedings of the Platform for Advanced Scientific Computing - {PASC} {\textquotesingle}16},
    doi = {10.1145/2929908.2929914},
    publisher = {{ACM} Press},
    title = {An Efficient Compressible Multicomponent Flow Solver for Heterogeneous {CPU}/{GPU} Architectures},
    url = {},
    year = {2016}


  • P. E. Hadjidoukas, D. Rossinelli, B. Hejazialhosseini, and P. Koumoutsakos, “From 11 to 14.4 PFLOPs: performance optimization for finite volume flow solver,” in Proceedings of the 3rd international conference on exascale applications and software – easc ’15, 2015, p. 7–12.
    [BibTeX] [PDF] [DOI]
    author = {Panagiotis E. Hadjidoukas and Diego Rossinelli and Babak Hejazialhosseini and Petros Koumoutsakos},
    booktitle = {Proceedings of the 3rd International Conference on Exascale Applications and Software – EASC '15},
    doi = {10.5555/2820083.2820085},
    note = {Proceedings of the 3rd International Conference on Exascale Applications and Software – {EASC} '15},
    pages = {7--12},
    publisher = {University of {E}dinburgh},
    title = {From 11 to 14.4 {PFLOPs}: Performance Optimization for Finite Volume Flow Solver},
    url = {},
    year = {2015}


  • D. Rossinelli, P. Koumoutsakos, B. Hejazialhosseini, P. Hadjidoukas, C. Bekas, A. Curioni, A. Bertsch, S. Futral, S. J. Schmidt, and N. A. Adams, “11 PFLOP/s simulations of cloud cavitation collapse,” in Proceedings of the international conference for high performance computing, networking, storage and analysis on – SC ’13, 2013.
    [BibTeX] [PDF] [DOI]
    author = {Diego Rossinelli and Petros Koumoutsakos and Babak Hejazialhosseini and Panagiotis Hadjidoukas and Costas Bekas and Alessandro Curioni and Adam Bertsch and Scott Futral and Steffen J. Schmidt and Nikolaus A. Adams},
    booktitle = {Proceedings of the International Conference for High Performance Computing, Networking, Storage and Analysis on - {SC} {\textquotesingle}13},
    doi = {10.1145/2503210.2504565},
    publisher = {{ACM} Press},
    title = {11 {PFLOP}/s simulations of cloud cavitation collapse},
    url = {},
    year = {2013}