A computational model of aquatic animal locomotion
Journal of Computational Physics
A computational model of the cochlea using the immersed boundary method
Journal of Computational Physics
Continuum models of platelet aggregation: formulation and mechanical properties
SIAM Journal on Applied Mathematics
SIAM Journal on Scientific and Statistical Computing
SIAM Journal on Numerical Analysis
Modeling biofilm processes using the immersed boundary method
Journal of Computational Physics
Immersed Interface Methods for Stokes Flow with Elastic Boundaries or Surface Tension
SIAM Journal on Scientific Computing
Simulating the motion of flexible pulp fibres using the immersed boundary method
Journal of Computational Physics
SIAM Journal on Numerical Analysis
Accurate projection methods for the incompressible Navier—Stokes equations
Journal of Computational Physics
The immersed interface method for the Navier-Stokes equations with singular forces
Journal of Computational Physics
Journal of Computational Physics
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
Journal of Computational Physics
SIAM Journal on Scientific Computing
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
SIAM Journal on Scientific Computing
A velocity decomposition approach for moving interfaces in viscous fluids
Journal of Computational Physics
Journal of Computational and Applied Mathematics
A second order virtual node method for elliptic problems with interfaces and irregular domains
Journal of Computational Physics
3D vesicle dynamics simulations with a linearly triangulated surface
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
A level-set continuum method for two-phase flows with insoluble surfactant
Journal of Computational Physics
Partially implicit motion of a sharp interface in Navier-Stokes flow
Journal of Computational Physics
Journal of Computational Physics
Approximation of Single Layer Distributions by Dirac Masses in Finite Element Computations
Journal of Scientific Computing
Hi-index | 31.50 |
This paper presents an implementation of the second-order accurate immersed interface method to simulate the motion of the flexible elastic membrane immersed in two viscous incompressible fluids with different viscosities, which further develops the work reported in Tan et al. [Z.-J. Tan, D.V. Le, K.M. Lim, B.C. Khoo, An Immersed Interface Method for the Incompressible Navier-Stokes Equations with Discontinuous Viscosity Across the Interface, submitted for publication] focussing mainly on the fixed interface problems. In this work, we introduce the velocity components at the membrane as two augmented unknown interface variables to decouple the originally coupled jump conditions for the velocity and pressure. Three forms of augmented equation are derived to determine the augmented variables to satisfy the continuous condition of the velocity. The velocity at the membrane, which determine the motion of the membrane, is then solved by the GMRES iterative method. The forces calculated from the configuration of the flexible elastic membrane and the augmented variables are interpolated using cubic splines and applied to the fluid through the jump conditions. The position of the flexible elastic membrane is updated implicitly using a quasi-Newton method (BFGS) within each time step. The Navier-Stokes equations are solved on a staggered Cartesian grid using a second order accurate projection method with the incorporation of spatial and temporal jump conditions. In addition, we also show that the inclusion of the temporal jump contributions has non-negligible effect on the simulation results when the grids are crossed by the membrane. Using the above method, we assess the effect of different viscosities on the flow solution and membrane motion.