Efficient implementation of essentially non-oscillatory shock-capturing schemes,II
Journal of Computational Physics
Incremental condition estimation
SIAM Journal on Matrix Analysis and Applications
Continuum models of platelet aggregation: formulation and mechanical properties
SIAM Journal on Applied Mathematics
Modeling a no-slip flow boundary with an external force field
Journal of Computational Physics
SIAM Journal on Numerical Analysis
Immersed Interface Methods for Stokes Flow with Elastic Boundaries or Surface Tension
SIAM Journal on Scientific Computing
GMRES On (Nearly) Singular Systems
SIAM Journal on Matrix Analysis and Applications
Preconditioned multigrid methods for unsteady incompressible flows
Journal of Computational Physics
Journal of Computational Physics
Computational methods for continuum models of platelet aggregation
Journal of Computational Physics
An accurate Cartesian grid method for viscous incompressible flows with complex immersed boundaries
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
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
A fast variational framework for accurate solid-fluid coupling
ACM SIGGRAPH 2007 papers
A direct-forcing fictitious domain method for particulate flows
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
Journal of Computational Physics
A new mathematical formulation and fast algorithm for fully resolved simulation of self-propulsion
Journal of Computational Physics
A well-conditioned augmented system for solving Navier-Stokes equations in irregular domains
Journal of Computational Physics
A velocity decomposition approach for moving interfaces in viscous fluids
Journal of Computational Physics
An immersed interface method for Stokes flows with fixed/moving interfaces and rigid boundaries
Journal of Computational Physics
An implicit immersed boundary method for three-dimensional fluid-membrane interactions
Journal of Computational Physics
A low numerical dissipation immersed interface method for the compressible Navier-Stokes equations
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
A boundary condition capturing immersed interface method for 3D rigid objects in a flow
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
Hi-index | 31.55 |
We present an immersed interface method for the incompressible Navier-Stokes equations capable of handling both rigid and flexible boundaries. The immersed boundaries are represented by a number of Lagrangian control points. In order to ensure that the no-slip condition on the rigid boundary is satisfied, singular forces are applied on the fluid. The forces are related to the jumps in pressure and the jumps in the derivatives of both pressure and velocity, and are interpolated using cubic splines. The strength of the singular forces at the rigid boundary is determined by solving a small system of equations at each timestep. For flexible boundaries, the forces that the boundary exerts on the fluid are computed from the constitutive relation of the flexible boundary and are applied to the fluid through the jump conditions. The position of the flexible boundary is updated implicitly using a quasi-Newton method (BFGS) within each timestep. The Navier-Stokes equations are discretized on a staggered Cartesian grid by a second order accurate projection method for pressure and velocity and the overall scheme is second order accurate.