Gerris: a tree-based adaptive solver for the incompressible Euler equations in complex geometries

Popinet, Stéphane

doi:10.1016/s0021-9991(03)00298-5

Cited by 1,097 publications

(897 citation statements)

References 41 publications

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“…As shown in Appendix A, errors in mass (or volume) conservation are very small in the present numerical methods (Popinet 2003(Popinet , 2009. We have checked here that, mass is conserved to better than 0.01% for both air and water for all resolutions tested and better than 0.001% in the highest resolution case (equivalent to 1024 3 , see Appendix A).…”

Section: Interface Reconstruction and Bubble Countingmentioning

confidence: 57%

“…We solve the three-dimensional two-phase incompressible Navier Stokes equations accounting for surface tension and viscous effects using the open source solver Gerris (Popinet 2003(Popinet , 2009), based on a quad/octree adaptive spatial discretization, multilevel Poisson solver. The interface between the high density liquid (water) and the low density gas (air) is reconstructed by a geometric Volume Of Fluid (VOF) method.…”

Section: The Gerris Flow Solvermentioning

confidence: 99%

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Air entrainment and bubble statistics in breaking waves

2016

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We investigate air entrainment and bubble statistics in three-dimensional breaking waves through novel direct numerical simulations of the two-phase air-water flow, resolving the length scales relevant for the bubble formation problem, the capillary length and the Hinze scale. The dissipation due to breaking is found to be in good agreement with previous experimental observations and inertial-scaling arguments. The air-entrainment properties and bubble-size statistics are investigated for various initial characteristic wave slopes. For radii larger than the Hinze scale, the bubble size distribution, can be described by N (r, t) = B(V 0 /2π)(ε(t − ∆τ )/W g)r −10/3 r −2/3 m during the active breaking stages, where ε(t − ∆τ ) is the time dependent turbulent dissipation rate, with ∆τ the collapse time of the initial air pocket entrained by the breaking wave, W a weighted vertical velocity of the bubble plume, r m the maximum bubble radius, g gravity, V 0 the initial volume of air entrained, r the bubble radius and B a dimensionless constant. The active breaking time-averaged bubble size distribution is described bȳ N (r) = B(1/2π)( l L c /W gρ)r −10/3 r −2/3 m , where l is the wave dissipation rate per unit length of breaking crest, ρ the water density and L c the length of breaking crest. Finally, the averaged total volume of entrained air,V , per breaking event can be simply related to l byV = B( l L c /W gρ), which leads to a relationship to a characteristic slope, S, of V ∝ S 5/2 . We propose a phenomenological turbulent bubble break-up model, based on earlier models and the balance between mechanical dissipation and work done against buoyancy forces. The model is consistent with the numerical results and existing experimental results.

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Section: Interface Reconstruction and Bubble Countingmentioning

confidence: 57%

Section: The Gerris Flow Solvermentioning

confidence: 99%

Air entrainment and bubble statistics in breaking waves

2016

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“…Several works have used this cell-centered approach for the simulation of fluids; see e.g. [110,81,80] and the references therein. We note that block structured AMR solvers, aided by efficient multigrid solvers (see [32] and the references therein), have advantages in that the entire grid structure may be stored efficiently, which may speed up the execution time.…”

Section: Introductionmentioning

confidence: 99%

High Resolution Sharp Computational Methods for Elliptic and Parabolic Problems in Complex Geometries

2012

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We present a review of some of the state-of-the-art numerical methods for solving the Stefan problem and the Poisson and the diffusion equations on irregular domains using (i) the level-set method for representing the (possibly moving) irregular domain's boundary, (ii) the ghost-fluid method for imposing the Dirichlet boundary condition at the irregular domain's boundary and (iii) a quadtree/octree nodebased adaptive mesh refinement for capturing small length scales while significantly reducing the memory and CPU footprint. In addition, we highlight common misconceptions and describe how to properly implement these methods. Numerical experiments illustrate quantitative and qualitative results.

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“…An open-source finite-volume code Gerris Flow Solver (Popinet, 2003) was used to model and solve this twophase fluid flow problem. As described above, the computational domain was taken as a square domain.…”

Section: Computational Proceduresmentioning

confidence: 99%

Numerical analysis of post-impact droplet deformation for direct-print

Hasan

Chandy

Choi

2015

Engineering Applications of Computational Fluid Mechanics

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Two-dimensional (2D) numerical investigations of droplet impacts on a solid surface and the consequent deformation have been performed. The application lies in the direct-print technology where droplets are used to create lines and instantly cured to maintain line dimension. The investigation focuses on the evolution of droplet shape at the initial stage after the impact for Newtonian fluids. More specifically, the investigation emphasized the time for an impacted droplet to start increasing its diameter after the initial compression due to impact. A computational model has been developed by utilizing an adaptive quadtree spatial discretization with piecewise-linear geometrical volume-of-fluid (VOF) for this multiphase problem. The continuum-surface-force method and the height-function (HF) were employed for estimating the surface tension and the interface curvature, respectively. The Gerris Flow Solver, an open-source finite-volume package, was used for developing the computational model. The investigation was performed for the governing parameters of the Froude number (Fr), Reynolds number (Re), and Weber number (We). The results are presented as the interface contour, spreading factor (ξ ), and deformation ratio (R δ ). The investigation shows that the results from the developed model have excellent agreement with the experimental results.

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Gerris: a tree-based adaptive solver for the incompressible Euler equations in complex geometries

Cited by 1,097 publications

References 41 publications

Air entrainment and bubble statistics in breaking waves

Air entrainment and bubble statistics in breaking waves

High Resolution Sharp Computational Methods for Elliptic and Parabolic Problems in Complex Geometries

Numerical analysis of post-impact droplet deformation for direct-print

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