Analysis of a one-dimensional model for the immersed boundary method
SIAM Journal on Numerical Analysis
A level set approach for computing solutions to incompressible two-phase flow
Journal of Computational Physics
SIAM Journal on Numerical Analysis
A level set formulation of Eulerian interface capturing methods for incompressible fluid flows
Journal of Computational Physics
Immersed Interface Methods for Stokes Flow with Elastic Boundaries or Surface Tension
SIAM Journal on Scientific Computing
A hybrid method for moving interface problems with application to the Hele-Shaw flow
Journal of Computational Physics
A Cartesian Grid Projection Method for the Incompressible Euler Equations in Complex Geometries
SIAM Journal on Scientific Computing
SIAM Journal on Numerical Analysis
A Fast Iterative Algorithm for Elliptic Interface Problems
SIAM Journal on Numerical Analysis
A Cartesian grid embedded boundary method for Poisson's equation on irregular domains
Journal of Computational Physics
A numerical method for solving incompressible flow problems with a surface of discontinuity
Journal of Computational Physics
A non-oscillatory Eulerian approach to interfaces in multimaterial flows (the ghost fluid method)
Journal of Computational Physics
Computation of solid-liquid phase fronts in the sharp interface limit on fixed grids
Journal of Computational Physics
SIAM Journal on Numerical Analysis
An immersed boundary method with formal second-order accuracy and reduced numerical viscosity
Journal of Computational Physics
Journal of Computational Physics
A Boundary Condition Capturing Method for Multiphase Incompressible Flow
Journal of Scientific Computing
The immersed interface method for the Navier-Stokes equations with singular forces
Journal of Computational Physics
A Cartesian grid embedded boundary method for the heat equation on irregular domains
Journal of Computational Physics
Interfacial dynamics for Stokes flow
Journal of Computational Physics
Level set methods: an overview and some recent results
Journal of Computational Physics
Journal of Computational Physics
A critical analysis of Rayleigh-Taylor growth rates
Journal of Computational Physics
A front-tracking method for the computations of multiphase flow
Journal of Computational Physics
A sharp interface Cartesian Ggid method for simulating flows with complex moving boundaries: 345
Journal of Computational Physics
Journal of Computational Physics
Maximum Principle Preserving Schemes for Interface Problems with Discontinuous Coefficients
SIAM Journal on Scientific Computing
The Immersed Interface/Multigrid Methods for Interface Problems
SIAM Journal on Scientific Computing
Immersed Interface Methods for Neumann and Related Problems in Two and Three Dimensions
SIAM Journal on Scientific Computing
Three-dimensional elliptic solvers for interface problems and applications
Journal of Computational Physics
Journal of Computational Physics
Solving a Nonlinear Problem in Magneto-Rheological Fluids Using the Immersed Interface Method
Journal of Scientific Computing
SIAM Journal on Scientific Computing
An Immersed Interface Method for Incompressible Navier-Stokes Equations
SIAM Journal on Scientific Computing
A cartesian grid method for modeling multiple moving objects in 2D incompressible viscous flow
Journal of Computational Physics
New Geometric Immersed Interface Multigrid Solvers
SIAM Journal on Scientific Computing
Numerical treatment of two-dimensional interfaces for acoustic and elastic waves
Journal of Computational Physics
Numerical approximations of singular source terms in differential equations
Journal of Computational Physics
Journal of Computational Physics
Discretization of Dirac delta functions in level set methods
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
Piecewise-polynomial discretization and Krylov-accelerated multigrid for elliptic interface problems
Journal of Computational Physics
Journal of Computational Physics
Effective stretching strategies for paraxial lightwave propagation simulations
Computers and Structures
A low numerical dissipation immersed interface method for the compressible Navier-Stokes equations
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
A novel concept for the design of immersed interface methods
Journal of Computational Physics
Mathematics and Computers in Simulation
Hi-index | 31.48 |
This paper presents a new high-order immersed interface method for elliptic equations with imbedded interface of discontinuity. Compared with the original second-order immersed interface method of [R.J. LeVeque, Z. Li. The immersed interface method for elliptic equations with discontinuous coefficients and singular sources. SIAM J. Numer. Anal. 31 (1994) 1001-25], the new method achieves arbitrarily high-order accuracy for derivatives at an irregular grid point by imposing only two physical jump conditions together with a wider set of grid stencils. The new interface difference formulas are expressed in a general explicit form so that they can be applied to different multi-dimensional problems without any modification. The new interface algorithms of up to O(h^4) accuracy have been derived and tested on several one and two-dimensional elliptic equations with imbedded interface. Compared to the standard second-order immersed interface method, the test results show that the new fourth-order immersed interface method leads to a significant improvement in accuracy of the numerical solutions. The proposed method has potential advantages in the application to two-phase flow because of its high-order accuracy and simplicity in applications.