A boundary condition capturing method for Poisson's equation on irregular domains

A Boundary Condition Capturing Method for Multiphase Incompressible Flow

Journal of Scientific Computing

A Cartesian grid method for solving the two-dimensional streamfunction-vorticity equations in irregular regions

Journal of Computational Physics

A second-order-accurate symmetric discretization of the Poisson equation on irregular domains

Journal of Computational Physics

Three-dimensional elliptic solvers for interface problems and applications

Journal of Computational Physics

Shock capturing, level sets, and PDE based methods in computer vision and image processing: a review of Osher's contributions

Journal of Computational Physics

An Eulerian method for computation of multimaterial impact with ENO shock-capturing and sharp interfaces

Journal of Computational Physics

A Level Set Approach for the Numerical Simulation of Dendritic Growth

Journal of Scientific Computing

Solving a Nonlinear Problem in Magneto-Rheological Fluids Using the Immersed Interface Method

Journal of Scientific Computing

Convergence of the ghost fluid method for elliptic equations with interfaces

Mathematics of Computation

A ghost-cell immersed boundary method for flow in complex geometry

Journal of Computational Physics

A thermodynamically consistent and fully conservative treatment of contact discontinuities for compressible multicomponent flows

Journal of Computational Physics

A numerical method for three-dimensional gas-liquid flow computations

Journal of Computational Physics

A decomposed immersed interface method for variable coefficient elliptic equations with non-smooth and discontinuous solutions

Journal of Computational Physics

Evolving interfaces via gradients of geometry-dependent interior Poisson problems: application to tumor growth

Journal of Computational Physics

A numerical method for solving variable coefficient elliptic equation with interfaces

Journal of Computational Physics

The embedded finite difference method for the Poisson equation in a domain with an irregular boundary and Dirichlet boundary conditions

Journal of Computational Physics

Discontinuous fluids

ACM SIGGRAPH 2005 Papers

Discretization of Dirac delta functions in level set methods

Journal of Computational Physics

Sharp interface Cartesian grid method I: An easily implemented technique for 3D moving boundary computations

Journal of Computational Physics

Sharp interface Cartesian grid method II: A technique for simulating droplet interactions with surfaces of arbitrary shape

Journal of Computational Physics

Sharp interface Cartesian grid method III: Solidification of pure materials and binary solutions

Journal of Computational Physics

A level-set method for interfacial flows with surfactant

Journal of Computational Physics

The numerical approximation of a delta function with application to level set methods

Journal of Computational Physics

High order matched interface and boundary method for elliptic equations with discontinuous coefficients and singular sources

Journal of Computational Physics

A balanced-force algorithm for continuous and sharp interfacial surface tension models within a volume tracking framework

Journal of Computational Physics

A Cartesian grid finite volume method for elliptic equations with variable coefficients and embedded interfaces

Journal of Computational Physics

Extrinsic meshfree approximation using asymptotic expansion for interfacial discontinuity of derivative

Journal of Computational Physics

A Level Set Method for vaporizing two-phase flows

Journal of Computational Physics

A level set based sharp interface method for the multiphase incompressible Navier-Stokes equations with phase change

Journal of Computational Physics

A Supra-Convergent Finite Difference Scheme for the Poisson and Heat Equations on Irregular Domains and Non-Graded Adaptive Cartesian Grids

Journal of Scientific Computing

Level Set Calculations for Incompressible Two-Phase Flows on a Dynamically Adaptive Grid

Journal of Scientific Computing

On Boundary Condition Capturing for Multiphase Interfaces

Journal of Scientific Computing

A large jump asymptotic framework for solving elliptic and parabolic equations with interfaces and strong coefficient discontinuities

Applied Numerical Mathematics

Derivative Particles for Simulating Detailed Movements of Fluids

IEEE Transactions on Visualization and Computer Graphics

A second order accurate level set method on non-graded adaptive cartesian grids

Journal of Computational Physics

An upwinding boundary condition capturing method for Maxwell's equations in media with material interfaces

Journal of Computational Physics

A coupling interface method for elliptic interface problems

Journal of Computational Physics

High order numerical methods to a type of delta function integrals

Journal of Computational Physics

Three-dimensional matched interface and boundary (MIB) method for treating geometric singularities

Journal of Computational Physics

A kernel-free boundary integral method for elliptic boundary value problems

Journal of Computational Physics

Short Note: A proof that a discrete delta function is second-order accurate

Journal of Computational Physics

A local directional ghost cell approach for incompressible viscous flow problems with irregular boundaries

Journal of Computational Physics

An adaptive ghost fluid finite volume method for compressible gas-water simulations

Journal of Computational Physics

An Improved Sharp Interface Method for Viscoelastic and Viscous Two-Phase Flows

Journal of Scientific Computing

An accurate conservative level set/ghost fluid method for simulating turbulent atomization

Journal of Computational Physics

A New Ghost Cell/Level Set Method for Moving Boundary Problems: Application to Tumor Growth

Journal of Scientific Computing

A Numerical Method for Free-Surface Flows and Its Application to Droplet Impact on a Thin Liquid Layer

Journal of Scientific Computing

HyPAM: A hybrid continuum-particle model for incompressible free-surface flows

Journal of Computational Physics

A spectrally refined interface approach for simulating multiphase flows

Journal of Computational Physics

Modeling merging and breakup in the moving mesh interface tracking method for multiphase flow simulations

Journal of Computational Physics

Immersed Interface Difference Schemes for a Parabolic-Elliptic Interface Problem

Large-Scale Scientific Computing

Numerical simulation of drop impact on a liquid-liquid interface with a multiple marker front-capturing method

Journal of Computational Physics

The adaptive immersed interface finite element method for elliptic and Maxwell interface problems

Journal of Computational Physics

A sharp interface finite volume method for elliptic equations on Cartesian grids

Journal of Computational Physics

An improved particle correction procedure for the particle level set method

Journal of Computational Physics

Sharp interface immersed-boundary/level-set method for wave-body interactions

Journal of Computational Physics

Guidelines for Poisson Solvers on Irregular Domains with Dirichlet Boundary Conditions Using the Ghost Fluid Method

Journal of Scientific Computing

A novel coupled level set and volume of fluid method for sharp interface capturing on 3D tetrahedral grids

Journal of Computational Physics

High order matched interface and boundary methods for the Helmholtz equation in media with arbitrarily curved interfaces

Journal of Computational Physics

An interpolation matched interface and boundary method for elliptic interface problems

Journal of Computational and Applied Mathematics

The Shortley-Weller embedded finite-difference method for the 3D Poisson equation with mixed boundary conditions

Journal of Computational Physics

Modeling and simulation of electronic structure, material interface and random doping in nano-electronic devices

Journal of Computational Physics

A second order virtual node method for elliptic problems with interfaces and irregular domains

Journal of Computational Physics

Numerical method for solving matrix coefficient elliptic equation with sharp-edged interfaces

Journal of Computational Physics

A ghost fluid, level set methodology for simulating multiphase electrohydrodynamic flows with application to liquid fuel injection

Journal of Computational Physics

An interface treating technique for compressible multi-medium flow with Runge-Kutta discontinuous Galerkin method

Journal of Computational Physics

Multiscale molecular dynamics using the matched interface and boundary method

Journal of Computational Physics

A Cartesian grid embedded boundary method for solving the Poisson and heat equations with discontinuous coefficients in three dimensions

Journal of Computational Physics

MIB method for elliptic equations with multi-material interfaces

Journal of Computational Physics

A simple multigrid scheme for solving the Poisson equation with arbitrary domain boundaries

Journal of Computational Physics

Simulations of multiphase flows with multiple length scales using moving mesh interface tracking with adaptive meshing

Journal of Computational Physics

Second-order Poisson-Nernst-Planck solver for ion transport

Journal of Computational Physics

Simulation of viscous flows with undulatory boundaries: Part II. Coupling with other solvers for two-fluid computations

Journal of Computational Physics

An immersed boundary method based on the lattice Boltzmann approach in three dimensions, with application

Computers & Mathematics with Applications

Physalis method for heterogeneous mixtures of dielectrics and conductors: Accurately simulating one million particles using a PC

Journal of Computational Physics

A second order virtual node method for elliptic problems with interfaces and irregular domains in three dimensions

Journal of Computational Physics

MultiFLIP for energetic two-phase fluid simulation

ACM Transactions on Graphics (TOG)

A level-set continuum method for two-phase flows with insoluble surfactant

Journal of Computational Physics

A second-order sharp numerical method for solving the linear elasticity equations on irregular domains and adaptive grids - Application to shape optimization

Journal of Computational Physics

Numerical modeling of thermocapillary two-phase flows with evaporation using a two-scalar approach for heat transfer

Journal of Computational Physics

Development of an immersed boundary-phase field-lattice Boltzmann method for Neumann boundary condition to study contact line dynamics

Journal of Computational Physics

A Family of Fourth-Order and Sixth-Order Compact Difference Schemes for the Three-Dimensional Poisson Equation

Journal of Scientific Computing

Heterogeneous mixtures of elliptical particles: Directly resolving local and global properties and responses

Journal of Computational Physics

A ghost fluid method for compressible reacting flows with phase change

Journal of Computational Physics

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

Journal of Scientific Computing

A weak formulation for solving elliptic interface problems without body fitted grid

Journal of Computational Physics

A second order virtual node algorithm for Stokes flow problems with interfacial forces, discontinuous material properties and irregular domains

Journal of Computational Physics

A kernel-free boundary integral method for implicitly defined surfaces

Journal of Computational Physics

A consistent and conservative scheme for MHD flows with complex boundaries on an unstructured Cartesian adaptive system

Journal of Computational Physics

A balanced-force algorithm for two-phase flows

Journal of Computational Physics

An asymptotic solution approach for elliptic equations with discontinuous coefficients

Journal of Computational Physics

Benchmarks and numerical methods for the simulation of boiling flows

Journal of Computational Physics