A Boundary Condition Capturing Method for Multiphase Incompressible Flow

By Myung-joo Kang, Ronald Fedkiw, Xu-Dong Liu. Journal of Scientific Computing, 2000

736 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/f4328c563af44f6e8e662b33aec99f3afef8a08c

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In Computational Mechanics

Citations in the corpus

Coupling water and smoke to thin deformable and rigid shells (2005, methodology): “[Kang et al. 2000] pointed out that smeared out pressures profiles (such as those used in the immersed boundary method) can cause parasitic currents when used to make the velocity divergence free (see also [Génevaux et al.”
Investigation of keyhole plume and molten pool based on a three-dimensional dynamic model with sharp interface formulation (2013, methodology): “To solve this problem, the sharp interface method [30, 31] has been applied in an LS-based model to simulate the keyhole, and the model is shown to be promising for a better prediction of keyhole dynamics.”
An accurate conservative level set/ghost fluid method for simulating turbulent atomization (2008, background): “While formulations have been proposed [23], they are not easy to implement, and an implicit formulation has proven challenging to develop.”
Spatially adaptive techniques for level set methods and incompressible flow (2006, methodology): “[50] illustrated that this technique is suitable for solving two-phase incompressible flow without smearing the density or pressure values across the interface.”
A level set based sharp interface method for the multiphase incompressible Navier-Stokes equations with phase change (2007, background): “This philosophy was then applied to a wide range of applications (see [5,9,12,19,21,22] and the references therein).”
Numerical Models of Surface Tension (2018, background): “Another type of surface tension discretisation usually associated with levelset interface representations is the Ghost Fluid Method (Fedkiw et al. 1999, Kang et al. 2000).”
[INVITED] An overview of the state of art in laser welding simulation (2016, methodology): “Some quite recent numerical techniques can be used to enhance the simulation of the boundary gap: the “sharp interface method” [35] or the “balanced forced method” [24].”
An unsteady single‐phase level set method for viscous free surface flows (2007, methodology): “The jump condition on any direction tangential to the free surface is [27]: (14) ( ) ( ) 0 μ μ ∇ ⋅ ⋅ + ∇ ⋅ ⋅ = ⎡⎣ v n t v t n⎤⎦ Neglecting the viscosity in air, and since t is an arbitrary vector perpendicular to the normal to the interface, we obtain the boundary conditions for the velocity at the ”
Numerical simulation of droplets, bubbles and waves: state of the art (2009, background): “Several schemes have been proposed to try to address some of these problems: for example both the “pressure gradient correction” scheme [18] and the “ghost-fluid method” [13] introduce better (and similar) discretisations of the pressure jump due to surface tension forces but do not address the disc”
A three-dimensional sharp interface model for self-consistent keyhole and weld pool dynamics in deep penetration laser welding (2011, methodology): “The boundary conditions (17) and (18) are treated using an accurate sharp interface method [27, 30].”
USING THE PARTICLE LEVEL SET METHOD AND A SECOND ORDER ACCURATE PRESSURE BOUNDARY CONDITION FOR FREE SURFACE FLOWS (2003, methodology): “Our treatment follows that presented in [11].”
An accurate adaptive solver for surface-tension-driven interfacial flows (2009, neutral): “1 AMS: 65M50; 76D05; 76D25; 76D45; 76M12; 76T10 Keywords: Adaptive mesh refinement; Surface tension; Navier-Stokes equations; Height-Function; Parasitic currents; Volume-Of-Fluid; Octree”
A balanced-force algorithm for continuous and sharp interfacial surface tension models within a volume tracking framework (2006, background): “E-mail address: mmfran@lanl.gov (M.M. Francois).”
A mass‐conserving Level‐Set method for modelling of multi‐phase flows (2005, methodology): “Since the Level-Set function and the VOF function are advected explicitly, the restriction due to advection is: tc = 1 |u|max= x + |v|max= y (50) The restriction due to surface tension given in Reference [23] is ts = 1 √ | |max=min( 0; 1)min( x; y)2 (51)”
A Fast Finite Differenc Method For Solving Navier-Stokes Equations on Irregular Domains (2003, methodology): “Among them are, just to name a few, Peskin’s immersed boundary method with numerous applications [7, 8, 11, 24, 28]; the ghost fluid method [15]; the immersed interface method [16]; the finite volume method [2, 26, 29, 32], etc.”
A review of level-set methods and some recent applications (2018, methodology): “Finally, it has been applied to flame fronts propagating in incompressible flows [103], to multiphase flows [104], for which a GFM approach to solve the Poisson equation with jump in the solution and its gradient [105] was introduced, and to multiphase flows with phase change [106].”