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Modeling and numerical approximation of twophase incompressible flows by a phasefield approach
"... Abstract. We present in this note a unified approach on how to design simple, efficient and energy stable time discretization schemes for the AllenCahn or CahnHilliard NavierStokes system which models twophase incompressible flows with matching or nonmatching density. Special emphasis is placed ..."
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Cited by 29 (7 self)
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Abstract. We present in this note a unified approach on how to design simple, efficient and energy stable time discretization schemes for the AllenCahn or CahnHilliard NavierStokes system which models twophase incompressible flows with matching or nonmatching density. Special emphasis is placed on designing schemes which only require solving linear systems at each time step while satisfy discrete energy laws that mimic the continuous energy laws. We construct the time discretization schemes in weak formulations so that they can be used with any consistent Galerkin type spacial discretization schemes such as finite element methods and spectral/spectralelement methods. Contents 1
Numerical simulation of droplets, bubbles and waves: state of the art
"... Abstract. This work present current advances in the numerical simulation of twophase flows using a VOF method, balancedforce surface tension and quad/octree adaptive mesh refinement. The simulations of the atomization of a liquid sheet, the capillary retraction of a liquid sheet and two and three ..."
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Cited by 16 (4 self)
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Abstract. This work present current advances in the numerical simulation of twophase flows using a VOF method, balancedforce surface tension and quad/octree adaptive mesh refinement. The simulations of the atomization of a liquid sheet, the capillary retraction of a liquid sheet and two and threedimensional wave breaking all for air/water systems, are used to show the potential of the numerical techniques. New simulations of atomization processes for air/water conditions are allowing to investigate the processes leading to the appearance of instabilities in the primary atomization zone in real conditions. For the retracting liquid sheet, the new simulations show that two different regimes can be encountered as a function of the Ohnesorge number. For large values, a laminar flow is encountered inside the rim and a steady state is reached after a quick transient state. For small values, a turbulent flow is generated inside the rim which is responsible of large oscillations in the rim size and neck thickness. The breaking wave case study demonstrates the ordersofmagnitude efficiency gains of the adaptive mesh refinement method.
Simulation of primary atomization with an octree adaptive mesh refinement and . . .
, 2008
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Quadtreeadaptive tsunami modelling
 Ocean Dynamics
, 2011
"... The wellbalanced, positivitypreserving scheme of Audusse et al, 2004, for the solution of the SaintVenant equations with wetting and drying, is generalised to an adaptive quadtree spatial discretisation. The scheme is validated using an analytical solution for the oscillation of a fluid in a para ..."
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Cited by 11 (1 self)
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The wellbalanced, positivitypreserving scheme of Audusse et al, 2004, for the solution of the SaintVenant equations with wetting and drying, is generalised to an adaptive quadtree spatial discretisation. The scheme is validated using an analytical solution for the oscillation of a fluid in a parabolic container, as well as the classic Monai tsunami laboratory benchmark. An efficient database system able to dynamically reconstruct a multiscale bathymetry based on extremely large datasets is also described. This combination of methods is sucessfully applied to the adaptive modelling of the 2004 Indian ocean tsunami. Adaptivity is shown to significantly decrease the exponent of the power law describing computational cost as a function of spatial resolution. The new exponent is directly related to the fractal dimension of the geometrical structures characterising tsunami propagation. The implementation of the method as well as the data and scripts necessary to reproduce the results presented are freely available as part of the opensource Gerris Flow Solver framework. 1
Adaptive momentoffluid method
 J. Comp. Phys
, 2009
"... This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. ..."
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Cited by 8 (0 self)
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This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. ACCEPTED MANUSCRIPT
A NUMERICAL METHOD FOR THE SIMULATION OF FREE SURFACE FLOWS OF VISCOPLASTIC FLUID IN 3D
, 2011
"... In this paper we study a numerical method for the simulation of free surface flows of viscoplastic (HerschelBulkley) fluids. The approach is based on the level set method for capturing the free surface evolution and on locally refined and dynamically adapted octree cartesian staggered grids for the ..."
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Cited by 7 (4 self)
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In this paper we study a numerical method for the simulation of free surface flows of viscoplastic (HerschelBulkley) fluids. The approach is based on the level set method for capturing the free surface evolution and on locally refined and dynamically adapted octree cartesian staggered grids for the discretization of fluid and level set equations. A regularized model is applied to handle the nondifferentiability of the constitutive relations. We consider an extension of the stable approximation of the Newtonian flow equations on staggered grid to approximate the viscoplastic model and levelset equations if the free boundary evolves and the mesh is dynamically refined or coarsened. The numerical method is first validated for a Newtonian case. In this case, the convergence of numerical solutions is observed towards experimental data when the mesh is refined. Further we compute several 3D viscoplastic HerschelBulkley fluid flows over incline planes for the dambreak problem. The qualitative comparison of numerical solutions is done versus experimental investigations. Another numerical example is given by computing the freely oscillating viscoplastic droplet, where the motion of fluid is driven by the surface tension forces. Altogether the considered techniques and algorithms (the levelset method, compact discretizations on dynamically adapted octree cartesian grids, regularization, and the surface tension forces approximation) result in efficient approach to modeling viscoplastic freesurface flows in possibly complex 3D geometries.
A Coupled Level SetMoment of Fluid Method for Incompressible TwoPhase Flows
"... A coupled level set and moment of fluid method (CLSMOF) is described for computing solutions to incompressible twophase flows. The local piecewise linear interface reconstruction (the CLSMOF reconstruction) uses information from ..."
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Cited by 4 (2 self)
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A coupled level set and moment of fluid method (CLSMOF) is described for computing solutions to incompressible twophase flows. The local piecewise linear interface reconstruction (the CLSMOF reconstruction) uses information from
An octreebased solver for the incompressible NavierStokes equations with enhanced stability and low dissipation.
"... The paper introduces a finite difference solver for the unsteady incompressible NavierStokes equations based on adaptive cartesian octree grids. The method extends a stable staggered grid finite difference scheme to the graded octree meshes. It is found that a straightforward extension is prone to ..."
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Cited by 3 (2 self)
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The paper introduces a finite difference solver for the unsteady incompressible NavierStokes equations based on adaptive cartesian octree grids. The method extends a stable staggered grid finite difference scheme to the graded octree meshes. It is found that a straightforward extension is prone to produce spurious oscillatory velocity modes on the finetocoarse grids interfaces. A local linear lowpass filter is shown to reduce much of the bad influence of the interface modes on the accuracy of numerical solution. We introduce an implicit upwind finite difference approximation of advective terms as a low dissipative and stable alternative to semiLagrangian methods to treat the transport part of the equations. The performance of method is verified for a set of benchmark tests: a Beltrami type flow, the 3D liddriven cavity and channel flows around the 3D square cylinder.
Multiscale simulations of primary atomization
, 2010
"... A liquid jet upon atomization breaks up in to small droplets that are orders of magnitude smaller than its diameter. Direct numerical simulations of atomization are exceedingly expensive computationally. Thus, the need to perform multiscale simulations. In the present study, we performed multiscale ..."
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Cited by 3 (1 self)
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A liquid jet upon atomization breaks up in to small droplets that are orders of magnitude smaller than its diameter. Direct numerical simulations of atomization are exceedingly expensive computationally. Thus, the need to perform multiscale simulations. In the present study, we performed multiscale simulations of primary atomization using a VolumeofFluid (VOF) algorithm coupled with a twoway coupling Lagrangian particletracking model to simulate the motion and influence of the smallest droplets. Collisions between two particles are efficiently predicted using a spatialhashing algorithm. The code is validated by comparing the numerical simulations for the motion of particles in several vortical structures with analytical solutions. We present simulations of the atomization of a liquid jet into droplets which are modeled as particles when away from the primary jet. We also present the probability density function of the droplets thus obtained and show the evolution of the PDF in space.
High Resolution Sharp Computational Methods for Elliptic and Parabolic Problems in Complex Geometries
, 2012
"... In honor of Stan Osher’s 70 th birthday We present a review of some of the stateoftheart numerical methods for solving the Stefan problem and the Poisson and the diffusion equations on irregular domains using (i) the levelset method for representing the (possibly moving) irregular domain’s bound ..."
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Cited by 2 (0 self)
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In honor of Stan Osher’s 70 th birthday We present a review of some of the stateoftheart numerical methods for solving the Stefan problem and the Poisson and the diffusion equations on irregular domains using (i) the levelset method for representing the (possibly moving) irregular domain’s boundary, (ii) the ghostfluid 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. 1