xGFM: recovering convergence of fluxes in the ghost fluid method
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Publication:778329
DOI10.1016/j.jcp.2020.109351zbMath1435.76050OpenAlexW3008539102MaRDI QIDQ778329
Publication date: 2 July 2020
Published in: Journal of Computational Physics (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.jcp.2020.109351
superconvergenceirregular domainsCartesian solverPoisson equation with jumps and/or discontinuous coefficients
Finite difference methods applied to problems in fluid mechanics (76M20) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Impulsive partial differential equations (35R12)
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Cites Work
- Unnamed Item
- A stable projection method for the incompressible Navier-Stokes equations on arbitrary geometries and adaptive quad/octrees
- Discretization of Dirac delta functions in level set methods
- Guidelines for Poisson solvers on irregular domains with Dirichlet boundary conditions using the ghost fluid method
- A correction function method for Poisson problems with interface jump conditions
- A finite element method for interface problems in domains with smooth boundaries and interfaces
- A numerical method for solving variable coefficient elliptic equation with interfaces
- A fourth order accurate discretization for the Laplace and heat equations on arbitrary domains, with applications to the Stefan problem
- A level set method for vaporizing two-phase flows
- A level set based sharp interface method for the multiphase incompressible Navier --- Stokes equations with phase change
- Robust second-order accurate discretizations of the multi-dimensional Heaviside and Dirac delta functions
- A non-oscillatory Eulerian approach to interfaces in multimaterial flows (the ghost fluid method)
- A note on immersed interface method for three-dimensional elliptic equations
- Finite element methods and their convergence for elliptic and parabolic interface problems
- A partial differential equation approach to multidimensional extrapolation.
- A second-order-accurate symmetric discretization of the Poisson equation on irregular domains
- High order solution of Poisson problems with piecewise constant coefficients and interface jumps
- An unfitted finite element method, based on Nitsche's method, for elliptic interface problems.
- A boundary condition capturing method for Poisson's equation on irregular domains
- Solving elliptic interface problems with jump conditions on Cartesian grids
- Solving Poisson-type equations with Robin boundary conditions on piecewise smooth interfaces
- A second-order boundary condition capturing method for solving the elliptic interface problems on irregular domains
- A ghost fluid/level set method for boiling flows and liquid evaporation: application to the leidenfrost effect
- High order matched interface and boundary method for elliptic equations with discontinuous coefficients and singular sources
- A supra-convergent finite difference scheme for the Poisson and heat equations on irregular domains and non-graded adaptive Cartesian grids
- The extended/generalized finite element method: An overview of the method and its applications
- p4est: Scalable Algorithms for Parallel Adaptive Mesh Refinement on Forests of Octrees
- An efficient finite element method for embedded interface problems
- Blending in the extended finite element method by discontinuous Galerkin and assumed strain methods
- The Immersed Interface Method for Elliptic Equations with Discontinuous Coefficients and Singular Sources
- Convergence of the ghost fluid method for elliptic equations with interfaces
- L<scp>EVEL</scp> S<scp>ET</scp> M<scp>ETHODS FOR</scp> F<scp>LUID</scp> I<scp>NTERFACES</scp>
- A Parallel Second Order Cartesian Method for Elliptic Interface Problems
- A finite element method for crack growth without remeshing
- Application of a level set method for simulation of droplet collisions
- The Fast Solution of Poisson’s and the Biharmonic Equations on Irregular Regions
- The Immersed Interface Method
- The Numerical Solution of Laplace's Equation
- A boundary condition capturing method for multiphase incompressible flow.
- The immersed interface method for the Navier-Stokes equations with singular forces
- A boundary condition capturing method for incompressible flame discontinuities.
