Special finite element methods for a class of second order elliptic problems with rough coefficients
SIAM Journal on Numerical Analysis
SIAM Journal on Numerical Analysis
A hybrid method for moving interface problems with application to the Hele-Shaw flow
Journal of Computational Physics
A Cartesian grid embedded boundary method for Poisson's equation on irregular domains
Journal of Computational Physics
A non-oscillatory Eulerian approach to interfaces in multimaterial flows (the ghost fluid method)
Journal of Computational Physics
A boundary condition capturing method for Poisson's equation on irregular domains
Journal of Computational Physics
Journal of Computational Physics
A second-order-accurate symmetric discretization of the Poisson equation on irregular domains
Journal of Computational Physics
A Particle-Partition of Unity Method for the Solution of Elliptic, Parabolic, and Hyperbolic PDEs
SIAM Journal on Scientific Computing
The Immersed Interface/Multigrid Methods for Interface Problems
SIAM Journal on Scientific Computing
Three-dimensional elliptic solvers for interface problems and applications
Journal of Computational Physics
Journal of Computational Physics
SIAM Journal on Scientific Computing
A numerical method for solving variable coefficient elliptic equation with interfaces
Journal of Computational Physics
A second-order method for three-dimensional particle simulation
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
Three-dimensional matched interface and boundary (MIB) method for treating geometric singularities
Journal of Computational Physics
A sharp interface finite volume method for elliptic equations on Cartesian grids
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
Hi-index | 31.45 |
In our earlier papers, Prosperetti's seminal Physalis method for fluid flows was extended to directly resolve electric fields in finite-sized particles and to investigate accurately the mutual fluid-particle, particle-particle, and particle-boundary interactions for circular/spherical particles. For the first time, the method makes the accurate prediction of the local charge distribution, force and torque on finite-sized particles possible. In the present work, the method is extended to heterogeneous mixtures of elliptical particles to further investigate the effects of the orientation and anisotropy. The direct resolution of the effect of fields in heterogeneous mixtures of elliptical particles to determine local and global properties and responses has many applications in engineering, mechanics, physics, chemistry, and biology. The method can be applied to heterogeneous materials, heterogeneous functional materials, microfluidics, and devices such as electric double layer capacitors. In the present paper, the accuracy of the method is extensively investigated even for very challenging problems, for example, for elongated rod-like particles with very high aspect ratios. The accuracy and efficiency of the method suggests that it can be used for many important applications of broad interest.