SIAM Journal on Scientific and Statistical Computing
Improved volume conservation in the computation of flows with immersed elastic boundaries
Journal of Computational Physics
Removing the stiffness from interfacial flows with surface tension
Journal of Computational Physics
Immersed Interface Methods for Stokes Flow with Elastic Boundaries or Surface Tension
SIAM Journal on Scientific Computing
Convergence Analysis for a Class of High-Order Semi-Lagrangian Advection Schemes
SIAM Journal on Numerical Analysis
The blob projection method for immersed boundary problems
Journal of Computational Physics
An efficient numerical method for studying interfacial motion in two-dimensional creeping flows
Journal of Computational Physics
The immersed interface method for the Navier-Stokes equations with singular forces
Journal of Computational Physics
A semi-Lagrangian high-order method for Navier-Stokes equations
Journal of Computational Physics
Maximum Principle Preserving Schemes for Interface Problems with Discontinuous Coefficients
SIAM Journal on Scientific Computing
An Immersed Interface Method for Incompressible Navier-Stokes Equations
SIAM Journal on Scientific Computing
Simulating the dynamics and interactions of flexible fibers in Stokes flows
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
The Immersed Interface Method: Numerical Solutions of PDEs Involving Interfaces and Irregular Domains (Frontiers in Applied Mathematics)
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
Locally corrected semi-Lagrangian methods for Stokes flow with moving elastic interfaces
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
Smoothing Properties of Implicit Finite Difference Methods for a Diffusion Equation in Maximum Norm
SIAM Journal on Numerical Analysis
Partially implicit motion of a sharp interface in Navier-Stokes flow
Journal of Computational Physics
Hi-index | 31.45 |
We present a second-order accurate method for computing the coupled motion of a viscous fluid and an elastic material interface with zero thickness. The fluid flow is described by the Navier-Stokes equations, with a singular force due to the stretching of the moving interface. We decompose the velocity into a ''Stokes'' part and a ''regular'' part. The first part is determined by the Stokes equations and the singular interfacial force. The Stokes solution is obtained using the immersed interface method, which gives second-order accurate values by incorporating known jumps for the solution and its derivatives into a finite difference method. The regular part of the velocity is given by the Navier-Stokes equations with a body force resulting from the Stokes part. The regular velocity is obtained using a time-stepping method that combines the semi-Lagrangian method with the backward difference formula. Because the body force is continuous, jump conditions are not necessary. For problems with stiff boundary forces, the decomposition approach can be combined with fractional time-stepping, using a smaller time step to advance the interface quickly by Stokes flow, with the velocity computed using boundary integrals. The small time steps maintain numerical stability, while the overall solution is updated on a larger time step to reduce computational cost.