Journal of Computational Physics
A three-dimensional computational method for blood flow in the heart. II. contractile fibers
Journal of Computational Physics
Multidimensional upwind methods for hyperbolic conservation laws
Journal of Computational Physics
SIAM Journal on Scientific Computing
On the stability of Godunov-projection methods for incompressible flow
Journal of Computational Physics
A projection method for locally refined grids
Journal of Computational Physics
Immersed Interface Methods for Stokes Flow with Elastic Boundaries or Surface Tension
SIAM Journal on Scientific Computing
Efficient management of parallelism in object-oriented numerical software libraries
Modern software tools for scientific computing
The Journal of Supercomputing - Special issue on supercomputing in medicine
Computational methods for continuum models of platelet aggregation
Journal of Computational Physics
An adaptive version of the immersed boundary method
Journal of Computational Physics
An immersed boundary method with formal second-order accuracy and reduced numerical viscosity
Journal of Computational Physics
A multigrid tutorial: second edition
A multigrid tutorial: second edition
The blob projection method for immersed boundary problems
Journal of Computational Physics
A cell-centered adaptive projection method for the incompressible Euler equations
Journal of Computational Physics
Accurate projection methods for the incompressible Navier—Stokes equations
Journal of Computational Physics
A Cartesian grid embedded boundary method for the heat equation on irregular domains
Journal of Computational Physics
The Method of Regularized Stokeslets
SIAM Journal on Scientific Computing
Approximate Projection Methods: Part I. Inviscid Analysis
SIAM Journal on Scientific Computing
A three-dimensional computer model of the human heart for studying cardiac fluid dynamics
ACM SIGGRAPH Computer Graphics
Simulation of a flapping flexible filament in a flowing soap film by the immersed boundary method
Journal of Computational Physics
hypre: A Library of High Performance Preconditioners
ICCS '02 Proceedings of the International Conference on Computational Science-Part III
Analysis and computation of immersed boundaries, with application to pulp fibres
Analysis and computation of immersed boundaries, with application to pulp fibres
An Immersed Interface Method for Incompressible Navier-Stokes Equations
SIAM Journal on Scientific Computing
Numerical approximations of singular source terms in differential equations
Journal of Computational Physics
An unsplit, cell-centered Godunov method for ideal MHD
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
Journal of Computational Physics
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
Three-dimensional matched interface and boundary (MIB) method for treating geometric singularities
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
Journal of Computational Physics
A new mathematical formulation and fast algorithm for fully resolved simulation of self-propulsion
Journal of Computational Physics
Simulating the dynamics of flexible bodies and vortex sheets
Journal of Computational Physics
A velocity decomposition approach for moving interfaces in viscous fluids
Journal of Computational Physics
Journal of Computational Physics
A lattice Boltzmann based implicit immersed boundary method for fluid-structure interaction
Computers & Mathematics with Applications
An interpolation matched interface and boundary method for elliptic interface problems
Journal of Computational and Applied Mathematics
Simulating the dynamics of inextensible vesicles by the penalty immersed boundary method
Journal of Computational Physics
Numerical simulations of two-dimensional foam by the immersed boundary method
Journal of Computational Physics
A conservative immersed interface method for Large-Eddy Simulation of incompressible flows
Journal of Computational Physics
A symmetric positive definite formulation for monolithic fluid structure interaction
Journal of Computational Physics
MIB method for elliptic equations with multi-material interfaces
Journal of Computational Physics
Computers & Mathematics with Applications
A boundary condition capturing immersed interface method for 3D rigid objects in a flow
Journal of Computational Physics
Journal of Computational Physics
Towards oscillation-free implementation of the immersed boundary method with spectral-like methods
Journal of Computational Physics
Partially implicit motion of a sharp interface in Navier-Stokes flow
Journal of Computational Physics
A Weak Formulation of the Immersed Boundary Method
SIAM Journal on Scientific Computing
Numerical simulations of two-dimensional wet foam by the immersed boundary method
Computers and Structures
Hi-index | 31.57 |
The immersed boundary method is both a mathematical formulation and a numerical scheme for problems involving the interaction of a viscous incompressible fluid and a (visco-)elastic structure. In [M.-C. Lai, Simulations of the flow past an array of circular cylinders as a test of the immersed boundary method, Ph.D. thesis, Courant Institute of Mathematical Sciences, New York University, 1998; M.-C. Lai, C.S. Peskin, An immersed boundary method with formal second-order accuracy and reduced numerical viscosity, J. Comput. Phys. 160 (2000) 705-719], Lai and Peskin introduced a formally second order accurate immersed boundary method, but the convergence properties of their algorithm have only been examined computationally for problems with nonsmooth solutions. Consequently, in practice only first order convergence rates have been observed. In the present work, we describe a new formally second order accurate immersed boundary method and demonstrate its performance for a prototypical fluid-structure interaction problem, involving an immersed viscoelastic shell of finite thickness, studied over a broad range of Reynolds numbers. We consider two sets of material properties for the viscoelastic structure, including a case where the material properties of the coupled system are discontinuous at the fluid-structure interface. For both sets of material properties, the true solutions appear to possess sufficient smoothness for the method to converge at a second order rate for fully resolved computations.