Numerical treatment of two-dimensional interfaces for acoustic and elastic waves
Journal of Computational Physics
A surfactant-conserving volume-of-fluid method for interfacial flows with insoluble surfactant
Journal of Computational Physics
Stability of approximate projection methods on cell-centered grids
Journal of Computational Physics
Short Note: A multi-phase flow method with a fast, geometry-based fluid indicator
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
A level-set method for interfacial flows with surfactant
Journal of Computational Physics
Journal of Computational Physics
An immersed interface method for simulating the interaction of a fluid with moving boundaries
Journal of Computational Physics
Moving overlapping grids with adaptive mesh refinement for high-speed reactive and non-reactive flow
Journal of Computational Physics
Journal of Computational Physics
Unconditionally stable discretizations of the immersed boundary equations
Journal of Computational Physics
An adaptive, formally second order accurate version of the immersed boundary method
Journal of Computational Physics
Matched interface and boundary (MIB) method for elliptic problems with sharp-edged interfaces
Journal of Computational Physics
Journal of Computational Physics
A coupling interface method for elliptic interface problems
Journal of Computational Physics
The immersed boundary method: A projection approach
Journal of Computational Physics
Three-dimensional matched interface and boundary (MIB) method for treating geometric singularities
Journal of Computational Physics
A fixed-mesh method for incompressible flow-structure systems with finite solid deformations
Journal of Computational Physics
Numerical prediction of interfacial instabilities: Sharp interface method (SIM)
Journal of Computational Physics
Locally corrected semi-Lagrangian methods for Stokes flow with moving elastic interfaces
Journal of Computational Physics
On the stability of the finite element immersed boundary method
Computers and Structures
Journal of Computational Physics
Journal of Computational Physics
International Journal of Computational Fluid Dynamics
Smoothed profile method for particulate flows: Error analysis and simulations
Journal of Computational Physics
Journal of Computational Physics
A velocity decomposition approach for moving interfaces in viscous fluids
Journal of Computational Physics
Modelling and simulation of porous immersed boundaries
Computers and Structures
Journal of Computational Physics
Prediction of wall-pressure fluctuation in turbulent flows with an immersed boundary method
Journal of Computational Physics
An immersed interface method for Stokes flows with fixed/moving interfaces and rigid boundaries
Journal of Computational Physics
A low numerical dissipation immersed interface method for the compressible Navier-Stokes equations
Journal of Computational Physics
A lattice Boltzmann based implicit immersed boundary method for fluid-structure interaction
Computers & Mathematics with Applications
GPU accelerated simulations of bluff body flows using vortex particle methods
Journal of Computational Physics
A spectral boundary integral method for flowing blood cells
Journal of Computational Physics
Journal of Computational Physics
A second order virtual node method for elliptic problems with interfaces and irregular domains
Journal of Computational Physics
Journal of Computational Physics
MIB method for elliptic equations with multi-material interfaces
Journal of Computational Physics
Simulations of single and multiple swimmers with non-divergence free deforming geometries
Journal of Computational Physics
Journal of Computational Physics
Semi-implicit formulation of the immersed finite element method
Computational Mechanics
Partially implicit motion of a sharp interface in Navier-Stokes flow
Journal of Computational Physics
Journal of Computational Physics
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The method developed in this paper is motivated by Peskin's immersed boundary (IB) method, and allows one to model the motion of flexible membranes or other structures immersed in viscous incompressible fluid using a fluid solver on a fixed Cartesian grid. The IB method uses a set of discrete delta functions to spread the entire singular force exerted by the immersed boundary to the nearby fluid grid points. Our method instead incorporates part of this force into jump conditions for the pressure, avoiding discrete dipole terms that adversely affect the accuracy near the immersed boundary. This has been implemented for the two-dimensional incompressible Navier--Stokes equations using a high-resolution finite-volume method for the advective terms and a projection method to enforce incompressibility. In the projection step, the correct jump in pressure is imposed in the course of solving the Poisson problem. This gives sharp resolution of the pressure across the interface and also gives better volume conservation than the traditional IB method. Comparisons between this method and the IB method are presented for several test problems. Numerical studies of the convergence and order of accuracy are included.