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Multiphase flows with sharp interfaces are found in many industrial applications and fundamental physics problems. For example, the study of fluidfuel interactions, bubbles and droplets, designing of sprays, boiling flows among others. This type of flows are usually referred as free surface and interfacial flows, since the contact of immiscible fluids or phases in motion produces a thin region that separates them called interface. In detail, interfacial flows are governed by the unsteady NavierStokes equations in the variabledensity incompressibility limit, additionally, they require the solution of a set of equations that describes the interface topology as it moves due to the velocity field. In order to accurately solve multiphase flows, the NavierStokes equations are fullyconservative discretized in terms of mass, momentum and kinetic energy. In detail, finitevolume numerical schemes, suitable for 3D unstructured meshes, are used to solve the momentum equations. Moreover, different interfacecapturing methods, such as: levelset, volumeoffluid and coupled levelset/volumeoffluid, are implemented to capture the topology of the phase interface as it evolves in time. 

Direct Numerical Simulation of GravityDriven Bubbly flows 

Gravitydriven bubbly flows play an important role in many natural and industrial processes. Steam generators in nuclear plants, unit operations in chemical engineering such as distillation, absorption, extraction, heterogeneous catalysis and bubble reactors are only a few among a multitude of applications that involve the motion of fluid particles (bubbles or droplets). These applications have motivated a large number of experimental investigations on bubble dynamics, moreover, the development of computers has promoted Direct Numerical Simulation (DNS) of the NavierStokes equations as another means of performing controlled experiments, providing a good way to noninvasive measure of bubble flows. Figure (1) illustrates some DNS examples of the rising motion of a swarm of bubbles in a vertical channel, carried out by means of a multiple marker levelset methodology introduced in [1, 2]. Simulations illustrated in Fig. (1) are performed as part of the 10thcall PRACE supercomputing project: “Direct Numerical Simulation of Gravity Driven Bubbly Flows” (see http://www.praceri.eu/prace10thprojectcall/ ).


Fig. 1: Direct numerical simulation of gravitydriven bubbly flows. 

Interfacecapturing methods and twophase flows 

There are multiple methods for DNS of twophase flows with sharp interfaces, for instance levelset and volumeoffluid methods. Although the idea behind these methods is similar, their numerical implementation may differ greatly, moreover, each method has advantages and disadvantages, therefore the development and improvement of interface capturing methodologies, and its application to the direct computation of twophase flows is an intense field of investigation over the last years. Regarding the aforementioned applications, some numerical methods, including their validation and verification, have been reported by the group in [14].




Fig. 2: Multiple marker levelset method. Droplet collision with a fluidfluid interface without coalescence. Detailed simulations have been reported in [1].




Fig. 3: Multiple marker levelset method. Binary droplet collision with bouncing outcome. Detailed simulations have been reported in [1].




Fig. 4: Interfacial flow with topology changes. Oblique coalescence of two deformable bubbles, computed by means of the finitevolume/levelset method introduced in [2]. (a) Time evolution of the bubble shape, (b) Velocity field




Figure 5: Interfacial flow with topology changes. Impact of a drop (water) fallen down into a liquid film (air as environment fluid). This simulation has been performed by means of the finitevolume/levelset method introduced in [2].




Fig. 6: Free surface flow. Collapse of a liquid column (water) in a rectangular container (air as environment fluid), computed by means of the finitevolume/levelset method introduced in [2].






Fig. 7: Free surface flow. Oscillating water column (OWC) system (air as environment fluid), computed by means of the finitevolume/levelset method introduced in [2]. (a) Unstructured mesh adapted to the complex domain, (b) Snapshot of the free surface/OCW interaction. 



Figure 8: RichtmyerMeshkov instability: Images of the experimental (top) and numerical simulation (bottom) of the 2D RichtmyerMeshkov instability. These simulations have been performed by means of the volumeoffluid method introduced in [3].




Fig. 9: RichtmyerMeshkov instability: Images of the experimental (top) and numerical simulation (bottom) of the 3D RichtmyerMeshkov instability. These simulations have been performed by means of the volumeoffluid method introduced in [3].


Publications 

On International Journals: [1] Balcázar, N., Jofre, L., Lehmkuhl, O., Castro, J., Rigola, J., A finitevolume/levelset method for simulating twophase flows on unstructured grids. International Journal of Multiphase Flow 64, September 2014, pp. 5572. https://doi.org/10.1016/j.ijmultiphaseflow.2014.04.008 [2] Balcázar, N., Lehmkuhl, O., Rigola, J., Oliva, A., A multiple marker levelset method for simulation of deformable fluid particles, International Journal of Multiphase Flow 74, September 2015, pp. 125142. https://doi.org/10.1016/j.ijmultiphaseflow.2015.04.009 [3] Balcázar, N., Lehmkuhl, O., Jofre, L., Oliva, A., Levelset simulations of buoyancydriven motion of single and multiple bubbles. International Journal of Heat and Fluid Flow, 56:91107, 2015. http://dx.doi.org/10.1016/j.ijheatfluidflow.2015.07.004 [4] Balcázar, N., Lehmkhul, O., Jofre, L., Rigola, J., Oliva, A. A coupled volumeoffluid/levelset method for simulation of twophase flows on unstructured meshes. Computers and Fluids 124, 1229, 2016. http://dx.doi.org/10.1016/j.compfluid.2015.10.005 [5] Balcázar, N., Rigola, J., Castro, J., Oliva, A., A levelset model for thermocapillary motion of deformable fluid particles, International Journal of Heat and Fluid Flow, Volume 62, Part B, 2016, pp 324343. http://dx.doi.org/10.1016/j.ijheatfluidflow.2016.09.015 [6] Jofre, L., Borrell, R., Lehmkuhl, O., Oliva, A., Parallel load balancing strategy for VolumeofFluid methods on 3D unstructured meshes. Journal of Computational Physics 282, 2015, pp. 269288 [7] Jofre, L., Lehmkuhl, O., Castro, J., Lluís Jofre, Oliva, A., A 3D VolumeofFluid advection method based on cellvertex velocities for unstructured meshes. Computers & Fluids 94. 2014, pp. 1429. [8] Schillaci, E., Jofre, L., Balcázar, N., Lehmkuhl, O., Oliva, A. A levelset aided singlephase model for the numerical simulation of freesurface flow on unstructured meshes, Computers & Fluids 140, 2016, 97110. http://dx.doi.org/10.1016/j.compfluid.2016.09.014 [9] Schillaci, E., Jofre, L., Balcázar, N., Antepara, O., Oliva, A. A lowdissipation convection scheme for the stable discretization of turbulent interfacial flow. Computers & Fluids 15. 2017, 102117. https://doi.org/10.1016/j.compfluid.2017.05.009 [10] E. Gutiérrez, N. Balcázar, E. Bartrons, J. Rigola. Numerical study of Taylor bubbles rising in a stagnant liquid using a levelset/movingmesh method. Chemical Engineering Science 164. 2017, 158177. https://doi.org/10.1016/j.ces.2017.02.018
On International Conference Proceedings: [11] Balcázar, N., Castro, J., Rigola, J., Oliva, A., DNS of the wall effect on the motion of bubble swarms. Procedia Computer Science 108, 2017, Pages 20082017. https://doi.org/10.1016/j.procs.2017.05.076 [12] Balcázar, N., Rigola, J., Oliva, A., A levelset method for thermal motion of bubbles and droplets. 7th European ThermalSciences Conference (Eurotherm2016). Journal of Physics: Conference Series 745 (2016) 032113. doi:10.1088/17426596/745/3/032113 [13] E. Gutiérrez, N. Balcázar, O. Lehmkuhl, A. Oliva.,^{ }On the solution of the full threedimensional Taylor bubble problem by using a coupled Conservative Level Set  Moving Mesh method. 7th European ThermalSciences Conference (Eurotherm2016). Journal of Physics: Conference Series 745 (2016) 032116. doi: 10.1088/17426596/745/3/032116 [14] Balcázar, N., Lehmkuhl, O., Castro, J., Rigola, J., Oliva, A., GRAVITYDRIVEN MOTION OF A SWARM OF BUBBLES IN A VERTICAL PIPE. 27th International Conference on Parallel Computational Fluid Dynamics, Parallel CFD2015. 2015. [15] Balcázar, N.; Jofre, L.; Lehmkuhl, O.; Castro, J.; Oliva, A., A multiple marker levelset method for simulation of bubbly flows. Proceedings of the jointly organized WCCM XI, ECCM V, ECFD VI. July 2025, 2014, Barcelona, Spain., pp. 52985309. [16] Jofre, L.; Balcázar, N.; Lehmkuhl, O.; Borrell, R.; Castro, J., Direct numerical simulation of the flow over a spherical bubble in a turbulent pipe flow. Proceedings of the jointly organized WCCM XI, ECCM V, ECFD VI., July 2025, 2014, Barcelona, Spain. pp. 53335343. [17] Schillaci, E.; Balcázar, N.; Lehmkuhl, O.; Jofre, L.; Oliva, A."A free surface model for the numerical simulation of oscillating water column systems".En: Proceedings of the jointly organized WCCM XI, ECCM V, ECFD VI. pp. 52865297. 2014. [18] Balcázar, N.; Jofre, L.; Lehmkuhl, O.; Rigola, J.; Castro, J.; Oliva, A., A finitevolume/levelset interface capturing method for unstructured grids: Simulations of bubbles rising through viscous liquids. Advances in Fluid Mechanics X, WIT Transactions on Engineering Sciences. pp. 239252. 2014. [19] Jofre, L.; Lehmkuhl, O.; Balcázar, N.; Castro, J.; Rigola, J.; Oliva, A, Conservative discretization of multiphase flow with high density ratios. Advances in Fluid Mechanics X, WIT Transactions on Engineering Sciences. pp. 153 – 164. 2014. [20] R. Borrell, L. Jofre, O. Lehmkuhl and J. Castro. Parallelization strategy for the volumeoffluid method on unstructured meshes. In Proceedings of the 25th International Conference on Parallel Computational Fluid Dynamics, 2013. [21] L. Jofre, N. Balcázar, O. Lehmkuhl, J. Castro and A. Oliva. Numerical study of the incompressible RichtmyerMeshkov instability. Interface tracking methods on general meshes. In Proceedings of the 15th International Conference on Fluid Flow Technologies, 2012. [22] N. Balcázar, L. Jofre, O. Lehmkuhl, J. Castro and A. Oliva. Numerical simulation of incompressible twophase flows by conservative levelset method. In Proceedings of the 15th International Conference on Fluid Flow Technologies, 2012. [23] L. Jofre, O. Lehmkuhl, J. Castro and A. Oliva. Vof/NavierStokes implementation on 3D unstructured staggered meshes. Application to the RichtmyerMeshkov instability. In Proceedings of the 7th International Conference on Computational Heat and Mass Transfer, 2011. [24] L. Jofre, O. Lehmkuhl, J. Castro and A. Oliva. A PlicVof implementation on parallel 3D unstructured meshes. In Proceedings of the 5th European Conference on Computational Fluid Dynamics, 2010.
