A Boundary Condition Capturing Method for Poisson's Equation on Irregular Domains

By Xu-Dong Liu, Ronald Fedkiw, Myung-joo Kang. 2000

698 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/9475493b6955ba0ef34ff0b6e2cf09f068de225f

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In Computational Mechanics

Citations in the corpus

Numerical simulation of unsteady multidimensional free surface motions by level set method (2003, background): “Surface tension can be either di used over the interface as a -functionlike volume force in the momentum equations [13] or exactly treated as a jump condition incorporated in the pressure Poisson equation [14, 15].”
A boundary condition capturing method for incompressible flame discontinuities (2001, methodology): “This method was designed as an extension of the Ghost Fluid Method [4] and relies heavily on the boundary condition capturing technology developed in [13] for the variable coefficient Poisson equation and in [12] for multiphase incompressible flow.”
A balanced-force algorithm for continuous and sharp interfacial surface tension models within a volume tracking framework (2006, methodology): “Recently, ghost fluid methods (GFMs) have been proposed in [15] to impose sharper boundary conditions on embedded boundaries.”
Level set methods: an overview and some recent results (2001, neutral): “A sample calculation from [49] is shown in figure 11 where one can see that both the solution, p, and its first derivatives are sharp across the interface without numerical smearing.”
A Boundary Condition Capturing Method for Multiphase Incompressible Flow (2000, methodology): “Then the techniques presented in [11] for the variable coefficient Poisson equation are used to solve equation 47 for the pressure at the grid nodes.”
Application of a level set method for simulation of droplet collisions (2005, methodology): “In the GFM methods, ghost cells are defined on each side of the interface (Liu et al., 2000; Kang et al., 2000) and appropriate schemes are applied for jump conditions.”
Meshfree point collocation method with intrinsic enrichment for interface problems (2007, methodology): “The order of convergence for the numerical solution u h is around O(h 1.8 ) which is comparable to those in other methods, for example, O(h 2 ) in the symmetric discretization method [24], O(h 1.4 ) in the boundary condition capturing method [ 25 ], O(h 2 ) in the fast iterative immersed interface m”
A second-order-accurate symmetric discretization of the Poisson equation on irregular domains (2002, methodology): “In this case, the solution is not coupled across the interface, and we are able to design a second order accurate symmetric discretization as opposed to the first order accurate discretization proposed in [20] for the jump condition case.”
A Cartesian Grid Method for Solving the Two-Dimensional Streamfunction-Vorticity Equations in Irregular Regions (2002, result): “Similar formulas can also be found in work by Liu and coworkers in [31], by Li and Lai, in [29], and by Wiegmann [51].”
The immersed interface method for the Navier-Stokes equations with singular forces (2001, methodology): “It was also derived independently in [29] for the ghost fluid method.”
Three-dimensional elliptic solvers for interface problems and applications (2003, methodology): “The problem can be solved by body fitted finite element methods, see [2], for one example; the ghost fluid method (GFM) [12] (which is first order accurate in the infinity norm but has a symmetric linear system); fast solvers based on integral equations (assuming β is a piecewise constant), see [4, ”
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.”
A level set based sharp interface method for the multiphase incompressible Navier-Stokes equations with phase change (2007, methodology): “This philosophy was then applied to a wide range of applications (see [5,9,12,19,21,22] and the references therein).”