A computational model of aquatic animal locomotion
Journal of Computational Physics
Journal of Computational Physics
Interaction of oscillating filaments: a computational study
Journal of Computational Physics
A numerical method for suspension flow
Journal of Computational Physics
Analysis of a one-dimensional model for the immersed boundary method
SIAM Journal on Numerical Analysis
Modeling a no-slip flow boundary with an external force field
Journal of Computational Physics
SIAM Journal on Numerical Analysis
Numerical simulation of a cylinder in uniform flow: application of a virtual boundary method
Journal of Computational Physics
The immersed interface method using a finite element formulation
Applied Numerical Mathematics
Modeling arteriolar flow and mass transport using the immersed boundary method
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
Combined immmersed-boundary finite-difference methods for three-dimensional complex flow simulations
Journal of Computational Physics
A comparison of spectral and vortex methods in three-dimensional incompressible flows
Journal of Computational Physics
Two-Dimensional Simulations of Valveless Pumping Using the Immersed Boundary Method
SIAM Journal on Scientific Computing
The Immersed Interface/Multigrid Methods for Interface Problems
SIAM Journal on Scientific Computing
Linearized pipe flow to Reynolds number 107
Journal of Computational Physics
An Immersed Interface Method for Incompressible Navier-Stokes Equations
SIAM Journal on Scientific Computing
A Jump Condition Capturing Finite Difference Scheme for Elliptic Interface Problems
SIAM Journal on Scientific Computing
New Geometric Immersed Interface Multigrid Solvers
SIAM Journal on Scientific Computing
Journal of Computational Physics
Numerical approximations of singular source terms in differential equations
Journal of Computational Physics
Journal of Computational Physics
Discretization of Dirac delta functions in level set methods
Journal of Computational Physics
Journal of Computational Physics
SIAM Journal on Scientific Computing
Journal of Computational Physics
An immersed interface method for simulating the interaction of a fluid with moving boundaries
Journal of Computational Physics
Journal of Computational Physics
A spectral fictitious domain method with internal forcing for solving elliptic PDEs
Journal of Computational Physics
Towards oscillation-free implementation of the immersed boundary method with spectral-like methods
Journal of Computational Physics
On the spectral accuracy of a fictitious domain method for elliptic operators in multi-dimensions
Journal of Computational Physics
Hi-index | 31.46 |
A global description of discontinuous functions is introduced in this paper. By expressing a discontinuous function as the sum of a smooth function and a correction term determined by jump conditions, we turn the unknown function from a discontinuous one into a sufficiently smooth one when solving a differential equation. Spectral schemes are developed based on this concept with the intention of eliminating or reducing the Gibbs oscillation. Finite difference schemes are also constructed as an alternative of the current immersed interface methods. Both spectral and finite difference schemes are tested on one- and two-dimensional cases.