Parallel simulation of multiphase flows using octree adaptivity and the volume-of-fluid method

Abstract We describe computations performed using the Gerris code, an open-source software implementing finite volume solvers on an octree adaptive grid together with a piecewise linear volume of fluid interface tracking method. The parallelisation of Gerris is achieved by domain decomposition. We show examples of the capabilities of Gerris on several types of problems. The impact of a droplet on a layer of the same liquid results in the formation of a thin air layer trapped between the droplet and the liquid layer that the adaptive refinement allows to capture. It is followed by the jetting of a thin corolla emerging from below the impacting droplet. The jet atomisation problem is another extremely challenging computational problem, in which a large number of small scales are generated. Finally we show an example of a turbulent jet computation in an equivalent resolution of 6 × 1024 3 cells. The jet simulation is based on the configuration of the Deepwater Horizon oil leak.

[1]  S. Zaleski,et al.  Droplet splashing on a thin liquid film , 2003 .

[2]  Frédéric Gibou,et al.  A level set based sharp interface method for the multiphase incompressible Navier-Stokes equations with phase change , 2007, J. Comput. Phys..

[3]  S. Popinet Gerris: a tree-based adaptive solver for the incompressible Euler equations in complex geometries , 2003 .

[4]  Deeparnab Chakrabarty,et al.  Knapsack Problems , 2008 .

[5]  Gretar Tryggvason,et al.  An Adaptive, Cartesian, Front-Tracking Method for the Motion, Deformation and Adhesion of Circulating Cells , 1998 .

[6]  P. Colella,et al.  An Adaptive Level Set Approach for Incompressible Two-Phase Flows , 1997 .

[7]  Matthew W. Williams,et al.  A balanced-force algorithm for continuous and sharp interfacial surface tension models within a volume tracking framework , 2006, J. Comput. Phys..

[8]  F. X. Demoulin,et al.  Numerical simulation of primary break-up and atomization: DNS and modelling study , 2009 .

[9]  Javad Mostaghimi,et al.  Air bubble entrapment under an impacting droplet , 2003 .

[10]  Stéphane Zaleski,et al.  Viscous versus inviscid instability of two-phase mixing layers with continuous velocity profile , 2005 .

[11]  Gretar Tryggvason,et al.  Direct Numerical Simulations of Gas–Liquid Multiphase Flows: Introduction , 2011 .

[12]  Philippe Marmottant,et al.  On spray formation , 2004, Journal of Fluid Mechanics.

[13]  Eugenio Aulisa,et al.  Interface reconstruction with least-squares fit and split advection in three-dimensional Cartesian geometry , 2007, J. Comput. Phys..

[14]  Danny Dolev,et al.  Fixing convergence of Gaussian belief propagation , 2009, 2009 IEEE International Symposium on Information Theory.

[15]  S. Zaleski,et al.  Numerical simulation of droplets, bubbles and waves: state of the art , 2009 .

[16]  Stéphane Popinet,et al.  An accurate adaptive solver for surface-tension-driven interfacial flows , 2009, J. Comput. Phys..

[17]  M. Tolstoy,et al.  Magnitude of the 2010 Gulf of Mexico Oil Leak , 2010, Science.

[18]  Jie Li,et al.  Calcul d'Interface Affine par Morceaux , 1995 .

[19]  O. Planchon,et al.  A Physical Model for the Action of Raindrop Erosion on Soil Microtopography , 2010 .

[20]  S. Zaleski,et al.  Interface reconstruction with least‐square fit and split Eulerian–Lagrangian advection , 2003 .

[21]  Sam Howison,et al.  Droplet impact on a thin fluid layer , 2005, Journal of Fluid Mechanics.

[22]  Jacques E. Boillat,et al.  Load Balancing and Poisson Equation in a Graph , 1990, Concurr. Pract. Exp..

[23]  Jack Louis Zable,et al.  Splatter during ink jet printing , 1977 .

[24]  S. Zaleski,et al.  A geometrical area-preserving volume-of-fluid advection method , 2003 .

[25]  Ralf Diekmann,et al.  Shape-optimized mesh partitioning and load balancing for parallel adaptive FEM , 2000, Parallel Comput..

[26]  Pascal Ray,et al.  Simulation of primary atomization with an octree adaptive mesh refinement and VOF method , 2009 .

[27]  Fares Ben Rayana Contribution à l'étude des instabilités interfaciales liquide-gaz en atomisation assistée et taille de gouttes , 2007 .

[28]  Michael P Brenner,et al.  Precursors to splashing of liquid droplets on a solid surface. , 2009, Physical review letters.

[29]  Sigurdur T. Thoroddsen,et al.  Air entrapment under an impacting drop , 2003, Journal of Fluid Mechanics.

[30]  Jie Li Piecewise linear interface calculation , 1995 .

[31]  D. R. Emerson,et al.  An optimal migration algorithm for dynamic load balancing , 1998, Concurr. Pract. Exp..

[32]  Gretar Tryggvason,et al.  Direct numerical simulations of gas/liquid multiphase flows , 2011 .